%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO023^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:08 AM UTC 2026
% Result : Theorem 7.41s 2.41s
% Output : Refutation 7.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PRO023^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:29:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.48 thf(spec,logic,$$dhol).
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 % File : PRO023^1 : TPTP v9.2.1. Released v7.0.0.
% 0.29/0.48 % Domain : Processes
% 0.29/0.48 % Problem : Process algebra 186
% 0.29/0.48 % Version : [Bla16] axioms : Especial.
% 0.29/0.48 % English :
% 0.29/0.48
% 0.29/0.48 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.29/0.48 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.29/0.48 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.29/0.48 % Source : [Bla16]
% 0.29/0.48 % Names : process__186.p [Bla16]
% 0.29/0.48
% 0.29/0.48 % Status : Theorem
% 0.29/0.48 % Rating : 0.33 v9.1.0, 0.00 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.29/0.48 % Syntax : Number of formulae : 316 ( 143 unt; 57 typ; 0 def)
% 0.29/0.48 % Number of atoms : 846 ( 424 equ; 0 cnn)
% 0.29/0.48 % Maximal formula atoms : 19 ( 3 avg)
% 0.29/0.48 % Number of connectives : 7470 ( 177 ~; 13 |; 55 &;6773 @)
% 0.29/0.48 % ( 0 <=>; 452 =>; 0 <=; 0 <~>)
% 0.29/0.48 % Maximal formula depth : 31 ( 11 avg)
% 0.29/0.48 % Number of types : 3 ( 2 usr)
% 0.29/0.48 % Number of type conns : 742 ( 742 >; 0 *; 0 +; 0 <<)
% 0.29/0.48 % Number of symbols : 58 ( 55 usr; 6 con; 0-14 aty)
% 0.29/0.48 % Number of variables : 1929 ( 205 ^;1617 !; 23 ?;1929 :)
% 0.29/0.48 % ( 84 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.48 % SPC : TH1_THM_EQU_NAR
% 0.29/0.48
% 0.29/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.48 % 2016-07-13 14:39:58.045
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 %----Could-be-implicit typings (7)
% 0.29/0.48 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 0.29/0.48 proces554692349s_term: $tType > $tType > $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 0.29/0.48 proces634752977rocess: $tType > $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.48 product_prod: $tType > $tType > $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_t_Set_Oset,type,
% 0.29/0.48 set: $tType > $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_t_itself,type,
% 0.29/0.48 itself: $tType > $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_tf_b,type,
% 0.29/0.48 b: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_tf_a,type,
% 0.29/0.48 a: $tType ).
% 0.29/0.48
% 0.29/0.48 %----Explicit typings (50)
% 0.29/0.48 thf(sy_c_HOL_Oundefined,type,
% 0.29/0.48 undefined:
% 0.29/0.48 !>[A: $tType] : A ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_If,type,
% 0.29/0.48 if:
% 0.29/0.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.29/0.48 bot_bot:
% 0.29/0.48 !>[A: $tType] : A ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 0.29/0.48 proces1239275103le_CH1:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 0.29/0.48 proces1869379930H1_rel:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 0.29/0.48 proces1239275104le_CH2:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 0.29/0.48 proces93903513H2_rel:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 0.29/0.48 proces126235999e_CONT:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 0.29/0.48 proces1004198490NT_rel:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 0.29/0.48 proces1708129104e_PREF:
% 0.29/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 0.29/0.48 proces527360425EF_rel:
% 0.29/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 0.29/0.48 proces1121166967uarded:
% 0.29/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 0.29/0.48 proces687458811_isACT:
% 0.29/0.48 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 0.29/0.48 proces896239806CT_rel:
% 0.29/0.48 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 0.29/0.48 proces1525233512Action:
% 0.29/0.48 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 0.29/0.48 proces1915862579Choice:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 0.29/0.48 proces1406508781rocess:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 0.29/0.48 proces979765041_ch1Of:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 0.29/0.48 proces988026546_ch2Of:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 0.29/0.48 proces1778668539contOf:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 0.29/0.48 proces894737309rocess:
% 0.29/0.48 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 0.29/0.48 proces10484146Action:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 0.29/0.48 proces401113213Choice:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 0.29/0.48 proces370407749rocess:
% 0.29/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 0.29/0.48 proces745025900prefOf:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 0.29/0.48 proces749077512rocess:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process,type,
% 0.29/0.48 proces1148692671rocess:
% 0.29/0.48 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( set @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 0.29/0.48 proces1454156180ss_ACT:
% 0.29/0.48 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 0.29/0.48 proces89589571ess_CH:
% 0.29/0.48 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 0.29/0.48 proces1062592052s_PROC:
% 0.29/0.48 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 0.29/0.48 proces1627516585ss_VAR:
% 0.29/0.48 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 0.29/0.48 proces460752237s_term:
% 0.29/0.48 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 0.29/0.48 proces224683037s_term:
% 0.29/0.48 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 0.29/0.48 proces2118920028s_term:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 0.29/0.48 proces2029722208s_term:
% 0.29/0.48 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset1__process__term,type,
% 0.29/0.48 proces1264666542s_term:
% 0.29/0.48 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 0.29/0.48 proces1493547885s_term:
% 0.29/0.48 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 0.29/0.48 proces1652378886lution:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Product__Type_OPair,type,
% 0.29/0.48 product_Pair:
% 0.29/0.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Pure_Otype,type,
% 0.29/0.48 type:
% 0.29/0.48 !>[A: $tType] : ( itself @ A ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Set_OCollect,type,
% 0.29/0.48 collect:
% 0.29/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Set_Oinsert,type,
% 0.29/0.48 insert:
% 0.29/0.48 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Set_Othe__elem,type,
% 0.29/0.48 the_elem:
% 0.29/0.48 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_Wellfounded_Oaccp,type,
% 0.29/0.48 accp:
% 0.29/0.48 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_c_member,type,
% 0.29/0.48 member:
% 0.29/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.48
% 0.29/0.48 thf(sy_v_p,type,
% 0.29/0.48 p: proces634752977rocess @ a ).
% 0.29/0.48
% 0.29/0.48 thf(sy_v_p_H____,type,
% 0.29/0.48 p2: proces634752977rocess @ a ).
% 0.29/0.48
% 0.29/0.48 thf(sy_v_pa____,type,
% 0.29/0.48 pa: proces634752977rocess @ a ).
% 0.29/0.48
% 0.29/0.48 thf(sy_v_q____,type,
% 0.29/0.48 q: proces634752977rocess @ a ).
% 0.29/0.48
% 0.29/0.48 thf(sy_v_sys,type,
% 0.29/0.48 sys: b > ( proces554692349s_term @ a @ b ) ).
% 0.29/0.48
% 0.29/0.48 %----Relevant facts (255)
% 0.29/0.48 thf(fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062,axiom,
% 0.29/0.48 ( ( proces10484146Action @ a @ pa )
% 0.29/0.48 | ( proces401113213Choice @ a @ pa ) ) ).
% 0.29/0.48
% 0.29/0.48 % \<open>isAction p \<or> isChoice p\<close>
% 0.29/0.48 thf(fact_1_process_Odistinct__disc_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ Process )
% 0.29/0.48 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.distinct_disc(2)
% 0.29/0.48 thf(fact_2_process_Odistinct__disc_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces10484146Action @ A @ Process )
% 0.29/0.48 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.distinct_disc(1)
% 0.29/0.48 thf(fact_3_isAction__isChoice,axiom,
% 0.29/0.48 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces10484146Action @ A @ P )
% 0.29/0.48 | ( proces401113213Choice @ A @ P ) ) ).
% 0.29/0.48
% 0.29/0.48 % isAction_isChoice
% 0.29/0.48 thf(fact_4_process_Oexhaust__disc,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ~ ( proces10484146Action @ A @ Process )
% 0.29/0.48 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.exhaust_disc
% 0.29/0.48 thf(fact_5_not__isAction__isChoice,axiom,
% 0.29/0.48 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.29/0.48 ~ ( ( proces10484146Action @ A @ P )
% 0.29/0.48 & ( proces401113213Choice @ A @ P ) ) ).
% 0.29/0.48
% 0.29/0.48 % not_isAction_isChoice
% 0.29/0.48 thf(fact_6_process_Ocorec__disc__iff_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( ~ ( P @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_disc_iff(2)
% 0.29/0.48 thf(fact_7_process_Ocorec__disc__iff_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 0.29/0.48 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( P @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_disc_iff(1)
% 0.29/0.48 thf(fact_8_iss,axiom,
% 0.29/0.48 ( p2
% 0.29/0.48 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % iss
% 0.29/0.48 thf(fact_9_process_Omap__disc__iff_I2_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( proces401113213Choice @ A @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_disc_iff(2)
% 0.29/0.48 thf(fact_10_process_Ocorec__disc_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ~ ( P @ A2 )
% 0.29/0.48 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_disc(2)
% 0.29/0.48 thf(fact_11_process_Omap__disc__iff_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( proces10484146Action @ A @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_disc_iff(1)
% 0.29/0.48 thf(fact_12_process_Ocorec__disc_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ( P @ A2 )
% 0.29/0.48 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_disc(1)
% 0.29/0.48 thf(fact_13_process_Odisc_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc(4)
% 0.29/0.48 thf(fact_14_process_Odisc_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc(3)
% 0.29/0.48 thf(fact_15_process_OdiscI_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Process
% 0.29/0.48 = ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.29/0.48 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.discI(2)
% 0.29/0.48 thf(fact_16_isChoice__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces401113213Choice @ A )
% 0.29/0.48 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.29/0.48 ? [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.29/0.48 ( Process2
% 0.29/0.48 = ( proces1915862579Choice @ A @ X212 @ X222 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isChoice_def
% 0.29/0.48 thf(fact_17_process_Odisc_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc(2)
% 0.29/0.48 thf(fact_18_process__term_Oinject_I2_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.29/0.48 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 0.29/0.48 = ( X2 = Y2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.inject(2)
% 0.29/0.48 thf(fact_19_process_Oinject_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( ( proces1525233512Action @ A @ X11 @ X12 )
% 0.29/0.48 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 0.29/0.48 = ( ( X11 = Y11 )
% 0.29/0.48 & ( X12 = Y12 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.inject(1)
% 0.29/0.48 thf(fact_20_process_Oinject_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( ( proces1915862579Choice @ A @ X21 @ X22 )
% 0.29/0.48 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 0.29/0.48 = ( ( X21 = Y21 )
% 0.29/0.48 & ( X22 = Y22 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.inject(2)
% 0.29/0.48 thf(fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 0.29/0.48 ( q
% 0.29/0.48 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % \<open>q = solution sys (PROC p)\<close>
% 0.29/0.48 thf(fact_22_process_Ocorec_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ~ ( P @ A2 )
% 0.29/0.48 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.29/0.48 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec(2)
% 0.29/0.48 thf(fact_23_process_Ocorec_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ( P @ A2 )
% 0.29/0.48 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.29/0.48 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec(1)
% 0.29/0.48 thf(fact_24_process_Osimps_I16_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.29/0.48 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X22 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.simps(16)
% 0.29/0.48 thf(fact_25_process_Osimps_I15_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F: A > B,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X12 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.simps(15)
% 0.29/0.48 thf(fact_26_process_Odistinct_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1525233512Action @ A @ X11 @ X12 )
% 0.29/0.48 != ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.distinct(1)
% 0.29/0.48 thf(fact_27_process_Oexhaust,axiom,
% 0.29/0.48 ! [A: $tType,Y: proces634752977rocess @ A] :
% 0.29/0.48 ( ! [X112: A,X122: proces634752977rocess @ A] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces1525233512Action @ A @ X112 @ X122 ) )
% 0.29/0.48 => ~ ! [X213: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces1915862579Choice @ A @ X213 @ X223 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.exhaust
% 0.29/0.48 thf(fact_28_process_Ocorec__code,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType] :
% 0.29/0.48 ( ( proces894737309rocess @ C @ A )
% 0.29/0.48 = ( ^ [P2: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A3: C] : ( if @ ( proces634752977rocess @ A ) @ ( P2 @ A3 ) @ ( proces1525233512Action @ A @ ( G112 @ A3 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A3 ) @ ( G1212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A3 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A3 ) @ ( G2112 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A3 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A3 ) @ ( G2212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A3 ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_code
% 0.29/0.48 thf(fact_29_process_Omap__ident,axiom,
% 0.29/0.48 ! [A: $tType,T: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces370407749rocess @ A @ A
% 0.29/0.48 @ ^ [X: A] : X
% 0.29/0.48 @ T )
% 0.29/0.48 = T ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_ident
% 0.29/0.48 thf(fact_30_process__strong__coind,axiom,
% 0.29/0.48 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ P @ P3 )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ P4 @ P5 )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ P4 )
% 0.29/0.48 = ( proces10484146Action @ A @ P5 ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ P4 )
% 0.29/0.48 = ( proces401113213Choice @ A @ P5 ) ) ) )
% 0.29/0.48 => ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
% 0.29/0.48 => ( ( A4 = A5 )
% 0.29/0.48 & ( ( Phi @ P4 @ P5 )
% 0.29/0.48 | ( P4 = P5 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
% 0.29/0.48 => ( ( ( Phi @ P4 @ P5 )
% 0.29/0.48 | ( P4 = P5 ) )
% 0.29/0.48 & ( ( Phi @ Q @ Q2 )
% 0.29/0.48 | ( Q = Q2 ) ) ) )
% 0.29/0.48 => ( P = P3 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_strong_coind
% 0.29/0.48 thf(fact_31_process__coind,axiom,
% 0.29/0.48 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ P @ P3 )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ P4 @ P5 )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ P4 )
% 0.29/0.48 = ( proces10484146Action @ A @ P5 ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ P4 )
% 0.29/0.48 = ( proces401113213Choice @ A @ P5 ) ) ) )
% 0.29/0.48 => ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
% 0.29/0.48 => ( ( A4 = A5 )
% 0.29/0.48 & ( Phi @ P4 @ P5 ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
% 0.29/0.48 => ( ( Phi @ P4 @ P5 )
% 0.29/0.48 & ( Phi @ Q @ Q2 ) ) )
% 0.29/0.48 => ( P = P3 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_coind
% 0.29/0.48 thf(fact_32_isAction__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces10484146Action @ A )
% 0.29/0.48 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.29/0.48 ? [X113: A,X123: proces634752977rocess @ A] :
% 0.29/0.48 ( Process2
% 0.29/0.48 = ( proces1525233512Action @ A @ X113 @ X123 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isAction_def
% 0.29/0.48 thf(fact_33_process_OdiscI_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Process
% 0.29/0.48 = ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 => ( proces10484146Action @ A @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.discI(1)
% 0.29/0.48 thf(fact_34_process_Odisc_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc(1)
% 0.29/0.48 thf(fact_35_solution_Odisc__iff_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.disc_iff(2)
% 0.29/0.48 thf(fact_36_solution_Odisc__iff_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.disc_iff(1)
% 0.29/0.48 thf(fact_37_solution_Odisc_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.disc(2)
% 0.29/0.48 thf(fact_38_solution_Odisc_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.disc(1)
% 0.29/0.48 thf(fact_39_process_Omap__sel_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.29/0.48 ( ( proces10484146Action @ A @ A2 )
% 0.29/0.48 => ( ( proces745025900prefOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( F @ ( proces745025900prefOf @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_sel(1)
% 0.29/0.48 thf(fact_40_process_Omap__sel_I3_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ A2 )
% 0.29/0.48 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_sel(3)
% 0.29/0.48 thf(fact_41_process_Omap__sel_I4_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ A2 )
% 0.29/0.48 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_sel(4)
% 0.29/0.48 thf(fact_42_isACT_Osimps_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 0.29/0.48 = ( proces10484146Action @ D @ P ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.simps(2)
% 0.29/0.48 thf(fact_43_process_Omap__sel_I2_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.29/0.48 ( ( proces10484146Action @ A @ A2 )
% 0.29/0.48 => ( ( proces1778668539contOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ F @ ( proces1778668539contOf @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_sel(2)
% 0.29/0.48 thf(fact_44_process_Odisc__eq__case_I2_J,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces401113213Choice @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ $o
% 0.29/0.48 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $false
% 0.29/0.48 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $true ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc_eq_case(2)
% 0.29/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,P6: A > $o] :
% 0.29/0.48 ( ( member @ A @ A2 @ ( collect @ A @ P6 ) )
% 0.29/0.48 = ( P6 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % mem_Collect_eq
% 0.29/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.48 ! [A: $tType,A6: set @ A] :
% 0.29/0.48 ( ( collect @ A
% 0.29/0.48 @ ^ [X: A] : ( member @ A @ X @ A6 ) )
% 0.29/0.48 = A6 ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_mem_eq
% 0.29/0.48 thf(fact_47_Collect__cong,axiom,
% 0.29/0.48 ! [A: $tType,P6: A > $o,Q3: A > $o] :
% 0.29/0.48 ( ! [X3: A] :
% 0.29/0.48 ( ( P6 @ X3 )
% 0.29/0.48 = ( Q3 @ X3 ) )
% 0.29/0.48 => ( ( collect @ A @ P6 )
% 0.29/0.48 = ( collect @ A @ Q3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_cong
% 0.29/0.48 thf(fact_48_ext,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.48 ( ! [X3: A] :
% 0.29/0.48 ( ( F @ X3 )
% 0.29/0.48 = ( G @ X3 ) )
% 0.29/0.48 => ( F = G ) ) ).
% 0.29/0.48
% 0.29/0.48 % ext
% 0.29/0.48 thf(fact_49_process_Ocollapse_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces10484146Action @ A @ Process )
% 0.29/0.48 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 0.29/0.48 = Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.collapse(1)
% 0.29/0.48 thf(fact_50_process_Ocollapse_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ Process )
% 0.29/0.48 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 0.29/0.48 = Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.collapse(2)
% 0.29/0.48 thf(fact_51_process_Osplit__sel,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.29/0.48 = ( ( ( Process
% 0.29/0.48 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.29/0.48 => ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.29/0.48 & ( ( Process
% 0.29/0.48 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.29/0.48 => ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.split_sel
% 0.29/0.48 thf(fact_52_process_Ocase__eq__if,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType] :
% 0.29/0.48 ( ( proces1406508781rocess @ A @ B )
% 0.29/0.48 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.case_eq_if
% 0.29/0.48 thf(fact_53_process_Osplit__sel__asm,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.29/0.48 = ( ~ ( ( ( Process
% 0.29/0.48 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.29/0.48 & ~ ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.29/0.48 | ( ( Process
% 0.29/0.48 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.29/0.48 & ~ ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.split_sel_asm
% 0.29/0.48 thf(fact_54_process_Oexhaust__sel,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( Process
% 0.29/0.48 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.29/0.48 => ( Process
% 0.29/0.48 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.exhaust_sel
% 0.29/0.48 thf(fact_55_process_Oexpand,axiom,
% 0.29/0.48 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( ( proces10484146Action @ A @ Process )
% 0.29/0.48 = ( proces10484146Action @ A @ Process3 ) )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ Process )
% 0.29/0.48 => ( ( proces10484146Action @ A @ Process3 )
% 0.29/0.48 => ( ( ( proces745025900prefOf @ A @ Process )
% 0.29/0.48 = ( proces745025900prefOf @ A @ Process3 ) )
% 0.29/0.48 & ( ( proces1778668539contOf @ A @ Process )
% 0.29/0.48 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 0.29/0.48 => ( ( ( proces401113213Choice @ A @ Process )
% 0.29/0.48 => ( ( proces401113213Choice @ A @ Process3 )
% 0.29/0.48 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 0.29/0.48 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 0.29/0.48 & ( ( proces988026546_ch2Of @ A @ Process )
% 0.29/0.48 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 0.29/0.48 => ( Process = Process3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.expand
% 0.29/0.48 thf(fact_56_process_Ocoinduct,axiom,
% 0.29/0.48 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( R @ Process @ Process3 )
% 0.29/0.48 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( R @ Process4 @ Process5 )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 = ( proces10484146Action @ A @ Process5 ) )
% 0.29/0.48 & ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 => ( ( proces10484146Action @ A @ Process5 )
% 0.29/0.48 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.29/0.48 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.29/0.48 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ Process4 )
% 0.29/0.48 => ( ( proces401113213Choice @ A @ Process5 )
% 0.29/0.48 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.29/0.48 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 0.29/0.48 => ( Process = Process3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.coinduct
% 0.29/0.48 thf(fact_57_process_Ocoinduct__strong,axiom,
% 0.29/0.48 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( R @ Process @ Process3 )
% 0.29/0.48 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.29/0.48 ( ( R @ Process4 @ Process5 )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 = ( proces10484146Action @ A @ Process5 ) )
% 0.29/0.48 & ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 => ( ( proces10484146Action @ A @ Process5 )
% 0.29/0.48 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.29/0.48 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.29/0.48 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 0.29/0.48 | ( ( proces1778668539contOf @ A @ Process4 )
% 0.29/0.48 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ Process4 )
% 0.29/0.48 => ( ( proces401113213Choice @ A @ Process5 )
% 0.29/0.48 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.29/0.48 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 0.29/0.48 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 0.29/0.48 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 0.29/0.48 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 0.29/0.48 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 0.29/0.48 => ( Process = Process3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.coinduct_strong
% 0.29/0.48 thf(fact_58_process_Ocase__distrib,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.29/0.48 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.29/0.48 = ( proces1406508781rocess @ A @ C
% 0.29/0.48 @ ^ [X1: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X1 @ X23 ) )
% 0.29/0.48 @ ^ [X1: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X1 @ X23 ) )
% 0.29/0.48 @ Process ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.case_distrib
% 0.29/0.48 thf(fact_59_process_Osel_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 = X12 ) ).
% 0.29/0.48
% 0.29/0.48 % process.sel(2)
% 0.29/0.48 thf(fact_60_process_Osel_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.29/0.48 = X21 ) ).
% 0.29/0.48
% 0.29/0.48 % process.sel(3)
% 0.29/0.48 thf(fact_61_process_Osel_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.29/0.48 = X22 ) ).
% 0.29/0.48
% 0.29/0.48 % process.sel(4)
% 0.29/0.48 thf(fact_62_process_Osel_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 = X11 ) ).
% 0.29/0.48
% 0.29/0.48 % process.sel(1)
% 0.29/0.48 thf(fact_63_process_Ocorec__sel_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ( P @ A2 )
% 0.29/0.48 => ( ( ( Q12 @ A2 )
% 0.29/0.48 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( G121 @ A2 ) ) )
% 0.29/0.48 & ( ~ ( Q12 @ A2 )
% 0.29/0.48 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_sel(2)
% 0.29/0.48 thf(fact_64_process_Ocorec__sel_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ~ ( P @ A2 )
% 0.29/0.48 => ( ( ( Q21 @ A2 )
% 0.29/0.48 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( G211 @ A2 ) ) )
% 0.29/0.48 & ( ~ ( Q21 @ A2 )
% 0.29/0.48 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_sel(3)
% 0.29/0.48 thf(fact_65_process_Ocorec__sel_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ~ ( P @ A2 )
% 0.29/0.48 => ( ( ( Q22 @ A2 )
% 0.29/0.48 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( G221 @ A2 ) ) )
% 0.29/0.48 & ( ~ ( Q22 @ A2 )
% 0.29/0.48 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_sel(4)
% 0.29/0.48 thf(fact_66_process_Ocorec__sel_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.29/0.48 ( ( P @ A2 )
% 0.29/0.48 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.29/0.48 = ( G11 @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.corec_sel(1)
% 0.29/0.48 thf(fact_67_process_Osimps_I5_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 = ( F1 @ X11 @ X12 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.simps(5)
% 0.29/0.48 thf(fact_68_process_Osimps_I6_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.29/0.48 = ( F2 @ X21 @ X22 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.simps(6)
% 0.29/0.48 thf(fact_69_process_Odisc__eq__case_I1_J,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces10484146Action @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ $o
% 0.29/0.48 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $true
% 0.29/0.48 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $false ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.disc_eq_case(1)
% 0.29/0.48 thf(fact_70_solution_Osimps_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.simps(3)
% 0.29/0.48 thf(fact_71_solution_Osimps_I5_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.simps(5)
% 0.29/0.48 thf(fact_72_solution_Osimps_I6_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.simps(6)
% 0.29/0.48 thf(fact_73_solution_Osimps_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.29/0.48 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.simps(4)
% 0.29/0.48 thf(fact_74_process_Orel__coinduct,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,P6: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 0.29/0.48 ( ( P6 @ X4 @ Y )
% 0.29/0.48 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 0.29/0.48 ( ( P6 @ Process4 @ Process5 )
% 0.29/0.48 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 = ( proces10484146Action @ B @ Process5 ) )
% 0.29/0.48 & ( ( proces10484146Action @ A @ Process4 )
% 0.29/0.48 => ( ( proces10484146Action @ B @ Process5 )
% 0.29/0.48 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 0.29/0.48 & ( P6 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ Process4 )
% 0.29/0.48 => ( ( proces401113213Choice @ B @ Process5 )
% 0.29/0.48 => ( ( P6 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 0.29/0.48 & ( P6 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 0.29/0.48 => ( proces749077512rocess @ A @ B @ R @ X4 @ Y ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_coinduct
% 0.29/0.48 thf(fact_75_process_Orel__sel,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B )
% 0.29/0.48 = ( ^ [R2: A > B > $o,A3: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 0.29/0.48 ( ( ( proces10484146Action @ A @ A3 )
% 0.29/0.48 = ( proces10484146Action @ B @ B2 ) )
% 0.29/0.48 & ( ( proces10484146Action @ A @ A3 )
% 0.29/0.48 => ( ( proces10484146Action @ B @ B2 )
% 0.29/0.48 => ( ( R2 @ ( proces745025900prefOf @ A @ A3 ) @ ( proces745025900prefOf @ B @ B2 ) )
% 0.29/0.48 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A3 ) @ ( proces1778668539contOf @ B @ B2 ) ) ) ) )
% 0.29/0.48 & ( ( proces401113213Choice @ A @ A3 )
% 0.29/0.48 => ( ( proces401113213Choice @ B @ B2 )
% 0.29/0.48 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A3 ) @ ( proces979765041_ch1Of @ B @ B2 ) )
% 0.29/0.48 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A3 ) @ ( proces988026546_ch2Of @ B @ B2 ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_sel
% 0.29/0.48 thf(fact_76_PREF_Osimps_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.29/0.48 = ( proces745025900prefOf @ B @ P ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.simps(2)
% 0.29/0.48 thf(fact_77_CH2_Osimps_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.simps(2)
% 0.29/0.48 thf(fact_78_process_Orel__inject_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 0.29/0.48 = ( ( R @ X11 @ Y11 )
% 0.29/0.48 & ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_inject(1)
% 0.29/0.48 thf(fact_79_process_Orel__inject_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 0.29/0.48 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.29/0.48 & ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_inject(2)
% 0.29/0.48 thf(fact_80_process_Orel__eq,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ A
% 0.29/0.48 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.29/0.48 = ( ^ [Y3: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y3 = Z ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_eq
% 0.29/0.48 thf(fact_81_process_Orel__refl,axiom,
% 0.29/0.48 ! [B: $tType,Ra: B > B > $o,X4: proces634752977rocess @ B] :
% 0.29/0.48 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.29/0.48 => ( proces749077512rocess @ B @ B @ Ra @ X4 @ X4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_refl
% 0.29/0.48 thf(fact_82_process_Orel__intros_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X12: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 0.29/0.48 ( ( R @ X11 @ Y11 )
% 0.29/0.48 => ( ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 )
% 0.29/0.48 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_intros(1)
% 0.29/0.48 thf(fact_83_process_Orel__intros_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X22: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.29/0.48 => ( ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 )
% 0.29/0.48 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_intros(2)
% 0.29/0.48 thf(fact_84_process_Orel__map_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,Sa: A > C > $o,X4: proces634752977rocess @ A,G: B > C,Y: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ C @ Sa @ X4 @ ( proces370407749rocess @ B @ C @ G @ Y ) )
% 0.29/0.48 = ( proces749077512rocess @ A @ B
% 0.29/0.48 @ ^ [X: A,Y4: B] : ( Sa @ X @ ( G @ Y4 ) )
% 0.29/0.48 @ X4
% 0.29/0.48 @ Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_map(2)
% 0.29/0.48 thf(fact_85_process_Orel__map_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,Sb: C > B > $o,I: A > C,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ C @ B @ Sb @ ( proces370407749rocess @ A @ C @ I @ X4 ) @ Y )
% 0.29/0.48 = ( proces749077512rocess @ A @ B
% 0.29/0.48 @ ^ [X: A] : ( Sb @ ( I @ X ) )
% 0.29/0.48 @ X4
% 0.29/0.48 @ Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_map(1)
% 0.29/0.48 thf(fact_86_solution_Ocode,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType] :
% 0.29/0.48 ( ( proces1652378886lution @ A @ B )
% 0.29/0.48 = ( ^ [Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys2 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces126235999e_CONT @ A @ B @ Sys2 @ T3 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275103le_CH1 @ A @ B @ Sys2 @ T3 ) ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275104le_CH2 @ A @ B @ Sys2 @ T3 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.code
% 0.29/0.48 thf(fact_87_process_Orel__distinct_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X12: proces634752977rocess @ B] :
% 0.29/0.48 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X12 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_distinct(2)
% 0.29/0.48 thf(fact_88_process_Orel__distinct_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.29/0.48 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_distinct(1)
% 0.29/0.48 thf(fact_89_process_Orel__cases,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B3: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B3 )
% 0.29/0.48 => ( ! [X13: A,X24: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1525233512Action @ A @ X13 @ X24 ) )
% 0.29/0.48 => ! [Y1: B,Y23: proces634752977rocess @ B] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces1525233512Action @ B @ Y1 @ Y23 ) )
% 0.29/0.48 => ( ( R @ X13 @ Y1 )
% 0.29/0.48 => ~ ( proces749077512rocess @ A @ B @ R @ X24 @ Y23 ) ) ) )
% 0.29/0.48 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 0.29/0.48 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 0.29/0.48 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 0.29/0.48 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_cases
% 0.29/0.48 thf(fact_90_solution_Octr_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.29/0.48 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.ctr(1)
% 0.29/0.48 thf(fact_91_solution_Octr_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.29/0.48 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.29/0.48 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution.ctr(2)
% 0.29/0.48 thf(fact_92_CONT_Osimps_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.simps(2)
% 0.29/0.48 thf(fact_93_CH1_Osimps_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH1.simps(2)
% 0.29/0.48 thf(fact_94_prefOf__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces745025900prefOf @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ A
% 0.29/0.48 @ ^ [X113: A,X123: proces634752977rocess @ A] : X113
% 0.29/0.48 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % prefOf_def
% 0.29/0.48 thf(fact_95_process_Oset__sel_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,A2: proces634752977rocess @ A,Xa: A] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ A2 )
% 0.29/0.48 => ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces979765041_ch1Of @ A @ A2 ) ) )
% 0.29/0.48 => ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_sel(3)
% 0.29/0.48 thf(fact_96_process_Oset__sel_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,A2: proces634752977rocess @ A,Xb: A] :
% 0.29/0.48 ( ( proces401113213Choice @ A @ A2 )
% 0.29/0.48 => ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces988026546_ch2Of @ A @ A2 ) ) )
% 0.29/0.48 => ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_sel(4)
% 0.29/0.48 thf(fact_97_process_Oset__sel_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,A2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces10484146Action @ A @ A2 )
% 0.29/0.48 => ( member @ A @ ( proces745025900prefOf @ A @ A2 ) @ ( proces1148692671rocess @ A @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_sel(1)
% 0.29/0.48 thf(fact_98_process_Oset__sel_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,A2: proces634752977rocess @ A,X4: A] :
% 0.29/0.48 ( ( proces10484146Action @ A @ A2 )
% 0.29/0.48 => ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
% 0.29/0.48 => ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_sel(2)
% 0.29/0.48 thf(fact_99_process_Oset__cases,axiom,
% 0.29/0.48 ! [A: $tType,E: A,A2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( member @ A @ E @ ( proces1148692671rocess @ A @ A2 ) )
% 0.29/0.48 => ( ! [Z2: proces634752977rocess @ A] :
% 0.29/0.48 ( A2
% 0.29/0.48 != ( proces1525233512Action @ A @ E @ Z2 ) )
% 0.29/0.48 => ( ! [Z1: A,Z2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) )
% 0.29/0.48 => ( ! [Z1: proces634752977rocess @ A] :
% 0.29/0.48 ( ? [Z2: proces634752977rocess @ A] :
% 0.29/0.48 ( A2
% 0.29/0.48 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z1 ) ) )
% 0.29/0.48 => ~ ! [Z1: proces634752977rocess @ A,Z2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_cases
% 0.29/0.48 thf(fact_100_process_Orel__refl__strong,axiom,
% 0.29/0.48 ! [A: $tType,X4: proces634752977rocess @ A,Ra: A > A > $o] :
% 0.29/0.48 ( ! [Z3: A] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 0.29/0.48 => ( Ra @ Z3 @ Z3 ) )
% 0.29/0.48 => ( proces749077512rocess @ A @ A @ Ra @ X4 @ X4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_refl_strong
% 0.29/0.48 thf(fact_101_process_Orel__mono__strong,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,R: A > B > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,Ra: A > B > $o] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
% 0.29/0.48 => ( ! [Z3: A,Yb: B] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 0.29/0.48 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y ) )
% 0.29/0.48 => ( ( R @ Z3 @ Yb )
% 0.29/0.48 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.29/0.48 => ( proces749077512rocess @ A @ B @ Ra @ X4 @ Y ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_mono_strong
% 0.29/0.48 thf(fact_102_process_Orel__cong,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,Y: proces634752977rocess @ B,Xa: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
% 0.29/0.48 ( ( X4 = Ya )
% 0.29/0.48 => ( ( Y = Xa )
% 0.29/0.48 => ( ! [Z3: A,Yb: B] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
% 0.29/0.48 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa ) )
% 0.29/0.48 => ( ( R @ Z3 @ Yb )
% 0.29/0.48 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.29/0.48 => ( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
% 0.29/0.48 = ( proces749077512rocess @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.rel_cong
% 0.29/0.48 thf(fact_103_process_Oset__intros_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,A1: A,A22: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_intros(1)
% 0.29/0.48 thf(fact_104_process_Oset__intros_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,A22: proces634752977rocess @ A,A1: A] :
% 0.29/0.48 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A22 ) )
% 0.29/0.48 => ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_intros(2)
% 0.29/0.48 thf(fact_105_process_Oset__intros_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,Xa: A,A1a: proces634752977rocess @ A,A2a: proces634752977rocess @ A] :
% 0.29/0.48 ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A1a ) )
% 0.29/0.48 => ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_intros(3)
% 0.29/0.48 thf(fact_106_process_Oset__intros_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,Xb: A,A2a: proces634752977rocess @ A,A1a: proces634752977rocess @ A] :
% 0.29/0.48 ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2a ) )
% 0.29/0.48 => ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_intros(4)
% 0.29/0.48 thf(fact_107_process_Oinj__map__strong,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Xa: proces634752977rocess @ A,F: A > B,Fa: A > B] :
% 0.29/0.48 ( ! [Z3: A,Za: A] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 0.29/0.48 => ( ( member @ A @ Za @ ( proces1148692671rocess @ A @ Xa ) )
% 0.29/0.48 => ( ( ( F @ Z3 )
% 0.29/0.48 = ( Fa @ Za ) )
% 0.29/0.48 => ( Z3 = Za ) ) ) )
% 0.29/0.48 => ( ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ Fa @ Xa ) )
% 0.29/0.48 => ( X4 = Xa ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.inj_map_strong
% 0.29/0.48 thf(fact_108_process_Omap__cong0,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,F: A > B,G: A > B] :
% 0.29/0.48 ( ! [Z3: A] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 0.29/0.48 => ( ( F @ Z3 )
% 0.29/0.48 = ( G @ Z3 ) ) )
% 0.29/0.48 => ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ G @ X4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_cong0
% 0.29/0.48 thf(fact_109_process_Omap__cong,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,F: A > B,G: A > B] :
% 0.29/0.48 ( ( X4 = Ya )
% 0.29/0.48 => ( ! [Z3: A] :
% 0.29/0.48 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
% 0.29/0.48 => ( ( F @ Z3 )
% 0.29/0.48 = ( G @ Z3 ) ) )
% 0.29/0.48 => ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 0.29/0.48 = ( proces370407749rocess @ A @ B @ G @ Ya ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.map_cong
% 0.29/0.48 thf(fact_110_contOf__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces1778668539contOf @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.29/0.48 @ ^ [X113: A,X123: proces634752977rocess @ A] : X123
% 0.29/0.48 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % contOf_def
% 0.29/0.48 thf(fact_111_ch1Of__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces979765041_ch1Of @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.29/0.48 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.29/0.48 @ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X212 ) ) ).
% 0.29/0.48
% 0.29/0.48 % ch1Of_def
% 0.29/0.48 thf(fact_112_ch2Of__def,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( proces988026546_ch2Of @ A )
% 0.29/0.48 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.29/0.48 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.29/0.48 @ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 0.29/0.48
% 0.29/0.48 % ch2Of_def
% 0.29/0.48 thf(fact_113_process_Oset__induct,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,A2: proces634752977rocess @ A,P6: A > ( proces634752977rocess @ A ) > $o] :
% 0.29/0.48 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) )
% 0.29/0.48 => ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P6 @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 0.29/0.48 => ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa2: A] :
% 0.29/0.48 ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ Z2 ) )
% 0.29/0.48 => ( ( P6 @ Xa2 @ Z2 )
% 0.29/0.48 => ( P6 @ Xa2 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
% 0.29/0.48 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb2: A] :
% 0.29/0.48 ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ Z1a ) )
% 0.29/0.48 => ( ( P6 @ Xb2 @ Z1a )
% 0.29/0.48 => ( P6 @ Xb2 @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 0.29/0.48 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc: A] :
% 0.29/0.48 ( ( member @ A @ Xc @ ( proces1148692671rocess @ A @ Z2a ) )
% 0.29/0.48 => ( ( P6 @ Xc @ Z2a )
% 0.29/0.48 => ( P6 @ Xc @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 0.29/0.48 => ( P6 @ X4 @ A2 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.set_induct
% 0.29/0.48 thf(fact_114_process_Osimps_I21_J,axiom,
% 0.29/0.48 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.29/0.48 = ( insert @ A @ X11 @ ( proces1148692671rocess @ A @ X12 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process.simps(21)
% 0.29/0.48 thf(fact_115_process__term_Osimps_I46_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.29/0.48 = ( proces1148692671rocess @ A @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(46)
% 0.29/0.48 thf(fact_116_process__term_Oset__intros_I1_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X4: A,Aa2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ Aa2 ) )
% 0.29/0.48 => ( member @ A @ X4 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ Aa2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_intros(1)
% 0.29/0.48 thf(fact_117_process__term_Osimps_I26_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,C: $tType,B: $tType,A: $tType,F1: A > B,F2: Pvar > C,X2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ C @ ( proces370407749rocess @ A @ B @ F1 @ X2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(26)
% 0.29/0.48 thf(fact_118_PREF_Osimps_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
% 0.29/0.48 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 0.29/0.48 = ( proces460752237s_term @ C @ B @ B
% 0.29/0.48 @ ^ [Aa3: C] : ( undefined @ B )
% 0.29/0.48 @ ( proces745025900prefOf @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.29/0.48 @ ( Sys @ X5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.simps(1)
% 0.29/0.48 thf(fact_119_process__term_Oinject_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,X14: Pvar,Y13: Pvar] :
% 0.29/0.48 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 0.29/0.48 = ( proces1627516585ss_VAR @ Pvar @ A @ Y13 ) )
% 0.29/0.48 = ( X14 = Y13 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.inject(1)
% 0.29/0.48 thf(fact_120_process__term_Ocase__distrib,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 0.29/0.48 = ( proces460752237s_term @ Pvar @ C @ A
% 0.29/0.48 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 0.29/0.48 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 0.29/0.48 @ ^ [X1: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X1 @ X23 ) )
% 0.29/0.48 @ ^ [X1: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X1 @ X23 ) )
% 0.29/0.48 @ Process_term ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.case_distrib
% 0.29/0.48 thf(fact_121_process__term_Omap__ident,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,T: proces554692349s_term @ A @ B] :
% 0.29/0.48 ( ( proces224683037s_term @ A @ A @ B @ B
% 0.29/0.48 @ ^ [X: A] : X
% 0.29/0.48 @ ^ [X: B] : X
% 0.29/0.48 @ T )
% 0.29/0.48 = T ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.map_ident
% 0.29/0.48 thf(fact_122_process__term_Osimps_I25_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X14: Pvar] :
% 0.29/0.48 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 0.29/0.48 = ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X14 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(25)
% 0.29/0.48 thf(fact_123_process__term_Osimps_I17_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X14: Pvar] :
% 0.29/0.48 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 0.29/0.48 = ( F1 @ X14 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(17)
% 0.29/0.48 thf(fact_124_process__term_Odistinct_I1_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X14: Pvar,X2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 0.29/0.48 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(1)
% 0.29/0.48 thf(fact_125_isACT_Osimps_I1_J,axiom,
% 0.29/0.48 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X5 ) )
% 0.29/0.48 = ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( Sys @ X5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.simps(1)
% 0.29/0.48 thf(fact_126_process__term_Osimps_I18_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.29/0.48 = ( F2 @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(18)
% 0.29/0.48 thf(fact_127_CONT_Osimps_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 0.29/0.48 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ( Sys @ X5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.simps(1)
% 0.29/0.48 thf(fact_128_CH2_Osimps_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 0.29/0.48 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 0.29/0.48 @ ( Sys @ X5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.simps(1)
% 0.29/0.48 thf(fact_129_CH1_Osimps_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 0.29/0.48 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 0.29/0.48 @ ( Sys @ X5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH1.simps(1)
% 0.29/0.48 thf(fact_130_insertCI,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.29/0.48 ( ( ~ ( member @ A @ A2 @ B4 )
% 0.29/0.48 => ( A2 = B3 ) )
% 0.29/0.48 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertCI
% 0.29/0.48 thf(fact_131_insert__iff,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,B3: A,A6: set @ A] :
% 0.29/0.48 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
% 0.29/0.48 = ( ( A2 = B3 )
% 0.29/0.48 | ( member @ A @ A2 @ A6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_iff
% 0.29/0.48 thf(fact_132_insert__absorb2,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,A6: set @ A] :
% 0.29/0.48 ( ( insert @ A @ X4 @ ( insert @ A @ X4 @ A6 ) )
% 0.29/0.48 = ( insert @ A @ X4 @ A6 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_absorb2
% 0.29/0.48 thf(fact_133_solution__VAR,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 0.29/0.48 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.29/0.48 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 0.29/0.48 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % solution_VAR
% 0.29/0.48 thf(fact_134_mk__disjoint__insert,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,A6: set @ A] :
% 0.29/0.48 ( ( member @ A @ A2 @ A6 )
% 0.29/0.48 => ? [B5: set @ A] :
% 0.29/0.48 ( ( A6
% 0.29/0.48 = ( insert @ A @ A2 @ B5 ) )
% 0.29/0.48 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % mk_disjoint_insert
% 0.29/0.48 thf(fact_135_insert__commute,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,Y: A,A6: set @ A] :
% 0.29/0.48 ( ( insert @ A @ X4 @ ( insert @ A @ Y @ A6 ) )
% 0.29/0.48 = ( insert @ A @ Y @ ( insert @ A @ X4 @ A6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_commute
% 0.29/0.48 thf(fact_136_insert__eq__iff,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,A6: set @ A,B3: A,B4: set @ A] :
% 0.29/0.48 ( ~ ( member @ A @ A2 @ A6 )
% 0.29/0.48 => ( ~ ( member @ A @ B3 @ B4 )
% 0.29/0.48 => ( ( ( insert @ A @ A2 @ A6 )
% 0.29/0.48 = ( insert @ A @ B3 @ B4 ) )
% 0.29/0.48 = ( ( ( A2 = B3 )
% 0.29/0.48 => ( A6 = B4 ) )
% 0.29/0.48 & ( ( A2 != B3 )
% 0.29/0.48 => ? [C2: set @ A] :
% 0.29/0.48 ( ( A6
% 0.29/0.48 = ( insert @ A @ B3 @ C2 ) )
% 0.29/0.48 & ~ ( member @ A @ B3 @ C2 )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert @ A @ A2 @ C2 ) )
% 0.29/0.48 & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_eq_iff
% 0.29/0.48 thf(fact_137_insert__absorb,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,A6: set @ A] :
% 0.29/0.48 ( ( member @ A @ A2 @ A6 )
% 0.29/0.48 => ( ( insert @ A @ A2 @ A6 )
% 0.29/0.48 = A6 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_absorb
% 0.29/0.48 thf(fact_138_insert__ident,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,A6: set @ A,B4: set @ A] :
% 0.29/0.48 ( ~ ( member @ A @ X4 @ A6 )
% 0.29/0.48 => ( ~ ( member @ A @ X4 @ B4 )
% 0.29/0.48 => ( ( ( insert @ A @ X4 @ A6 )
% 0.29/0.48 = ( insert @ A @ X4 @ B4 ) )
% 0.29/0.48 = ( A6 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_ident
% 0.29/0.48 thf(fact_139_Set_Oset__insert,axiom,
% 0.29/0.48 ! [A: $tType,X4: A,A6: set @ A] :
% 0.29/0.48 ( ( member @ A @ X4 @ A6 )
% 0.29/0.48 => ~ ! [B5: set @ A] :
% 0.29/0.48 ( ( A6
% 0.29/0.48 = ( insert @ A @ X4 @ B5 ) )
% 0.29/0.48 => ( member @ A @ X4 @ B5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Set.set_insert
% 0.29/0.48 thf(fact_140_insertI2,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.29/0.48 ( ( member @ A @ A2 @ B4 )
% 0.29/0.48 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI2
% 0.29/0.48 thf(fact_141_insertI1,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI1
% 0.29/0.48 thf(fact_142_insertE,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,B3: A,A6: set @ A] :
% 0.29/0.48 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
% 0.29/0.48 => ( ( A2 != B3 )
% 0.29/0.48 => ( member @ A @ A2 @ A6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertE
% 0.29/0.48 thf(fact_143_guarded__def,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,A: $tType] :
% 0.29/0.48 ( ( proces1121166967uarded @ A @ B @ C )
% 0.29/0.48 = ( ^ [Sys2: A > ( proces554692349s_term @ B @ C )] :
% 0.29/0.48 ! [X6: A,Y5: C] :
% 0.29/0.48 ( ( Sys2 @ X6 )
% 0.29/0.48 != ( proces1627516585ss_VAR @ C @ B @ Y5 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % guarded_def
% 0.29/0.48 thf(fact_144_insert__compr,axiom,
% 0.29/0.48 ! [A: $tType] :
% 0.29/0.48 ( ( insert @ A )
% 0.29/0.48 = ( ^ [A3: A,B6: set @ A] :
% 0.29/0.48 ( collect @ A
% 0.29/0.48 @ ^ [X: A] :
% 0.29/0.48 ( ( X = A3 )
% 0.29/0.48 | ( member @ A @ X @ B6 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_compr
% 0.29/0.48 thf(fact_145_insert__Collect,axiom,
% 0.29/0.48 ! [A: $tType,A2: A,P6: A > $o] :
% 0.29/0.48 ( ( insert @ A @ A2 @ ( collect @ A @ P6 ) )
% 0.29/0.48 = ( collect @ A
% 0.29/0.48 @ ^ [U: A] :
% 0.29/0.48 ( ( U != A2 )
% 0.29/0.48 => ( P6 @ U ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_Collect
% 0.29/0.48 thf(fact_146_isACT__VAR,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 0.29/0.48 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.29/0.48 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X5 ) )
% 0.29/0.48 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT_VAR
% 0.29/0.48 thf(fact_147_isACT_Oelims_I2_J,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ~ ( proces10484146Action @ D @ P4 ) )
% 0.29/0.48 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 != ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.elims(2)
% 0.29/0.48 thf(fact_148_isACT_Oelims_I3_J,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( proces10484146Action @ D @ P4 ) )
% 0.29/0.48 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.elims(3)
% 0.29/0.48 thf(fact_149_CH2_Oelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 0.29/0.48 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( Y != T23 ) )
% 0.29/0.48 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.elims
% 0.29/0.48 thf(fact_150_CH1_Oelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 0.29/0.48 => ( ! [T12: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ? [T23: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( Y != T12 ) )
% 0.29/0.48 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH1.elims
% 0.29/0.48 thf(fact_151_process__term_Oinject_I4_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 0.29/0.48 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 0.29/0.48 = ( ( X41 = Y41 )
% 0.29/0.48 & ( X42 = Y42 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.inject(4)
% 0.29/0.48 thf(fact_152_process__term_Oinject_I3_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.29/0.48 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 0.29/0.48 = ( ( X31 = Y31 )
% 0.29/0.48 & ( X32 = Y32 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.inject(3)
% 0.29/0.48 thf(fact_153_process__term_Osimps_I47_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.29/0.48 = ( insert @ A @ X31 @ ( proces1264666542s_term @ A @ Pvar @ X32 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(47)
% 0.29/0.48 thf(fact_154_process__term_Osimps_I20_J,axiom,
% 0.29/0.48 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.29/0.48 = ( F4 @ X41 @ X42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(20)
% 0.29/0.48 thf(fact_155_isACT_Osimps_I4_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T13: proces554692349s_term @ D @ A,T24: proces554692349s_term @ D @ A] :
% 0.29/0.48 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T13 @ T24 ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.simps(4)
% 0.29/0.48 thf(fact_156_process__term_Osimps_I19_J,axiom,
% 0.29/0.48 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.29/0.48 = ( F3 @ X31 @ X32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(19)
% 0.29/0.48 thf(fact_157_isACT_Osimps_I3_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.simps(3)
% 0.29/0.48 thf(fact_158_process__term_Odistinct_I11_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.29/0.48 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(11)
% 0.29/0.48 thf(fact_159_process__term_Odistinct_I7_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.29/0.48 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(7)
% 0.29/0.48 thf(fact_160_process__term_Odistinct_I9_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.29/0.48 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(9)
% 0.29/0.48 thf(fact_161_process__term_Oset__intros_I2_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,A1: A,A22: proces554692349s_term @ A @ Pvar] : ( member @ A @ A1 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_intros(2)
% 0.29/0.48 thf(fact_162_process__term_Oset__intros_I3_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,Xa: A,A22: proces554692349s_term @ A @ Pvar,A1: A] :
% 0.29/0.48 ( ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ A22 ) )
% 0.29/0.48 => ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_intros(3)
% 0.29/0.48 thf(fact_163_process__term_Oset__intros_I4_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,Xc2: A,A1a: proces554692349s_term @ A @ Pvar,A2a: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ A1a ) )
% 0.29/0.48 => ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_intros(4)
% 0.29/0.48 thf(fact_164_process__term_Oset__intros_I5_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,Xe: A,A2a: proces554692349s_term @ A @ Pvar,A1a: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ A2a ) )
% 0.29/0.48 => ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_intros(5)
% 0.29/0.48 thf(fact_165_process__term_Odistinct_I3_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X14: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 0.29/0.48 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(3)
% 0.29/0.48 thf(fact_166_process__term_Odistinct_I5_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,X14: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 0.29/0.48 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.distinct(5)
% 0.29/0.48 thf(fact_167_process__term_Osimps_I27_J,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ C @ ( F1 @ X31 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X32 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(27)
% 0.29/0.48 thf(fact_168_process__term_Osimps_I28_J,axiom,
% 0.29/0.48 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.29/0.48 = ( proces89589571ess_CH @ B @ C @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X41 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X42 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.simps(28)
% 0.29/0.48 thf(fact_169_process__term_Oexhaust,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,Y: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ! [X13: Pvar] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 0.29/0.48 => ( ! [X24: proces634752977rocess @ A] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces1062592052s_PROC @ A @ Pvar @ X24 ) )
% 0.29/0.48 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 0.29/0.48 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( Y
% 0.29/0.48 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.exhaust
% 0.29/0.48 thf(fact_170_process__term_Oinduct,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,P6: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ! [X3: Pvar] : ( P6 @ ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
% 0.29/0.48 => ( ! [X3: proces634752977rocess @ A] : ( P6 @ ( proces1062592052s_PROC @ A @ Pvar @ X3 ) )
% 0.29/0.48 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( P6 @ X2a )
% 0.29/0.48 => ( P6 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 0.29/0.48 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( P6 @ X1a )
% 0.29/0.48 => ( ( P6 @ X2a )
% 0.29/0.48 => ( P6 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 0.29/0.48 => ( P6 @ Process_term ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.induct
% 0.29/0.48 thf(fact_171_isACT_Oinduct,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,P6: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.induct
% 0.29/0.48 thf(fact_172_PREF_Oinduct,axiom,
% 0.29/0.48 ! [C: $tType,A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.induct
% 0.29/0.48 thf(fact_173_CONT_Oinduct,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.induct
% 0.29/0.48 thf(fact_174_CH2_Oinduct,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.induct
% 0.29/0.48 thf(fact_175_CH1_Osimps_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
% 0.29/0.48 = T13 ) ).
% 0.29/0.48
% 0.29/0.48 % CH1.simps(3)
% 0.29/0.48 thf(fact_176_CH2_Osimps_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
% 0.29/0.48 = T24 ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.simps(3)
% 0.29/0.48 thf(fact_177_CONT_Osimps_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.29/0.48 = T2 ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.simps(3)
% 0.29/0.48 thf(fact_178_PREF_Osimps_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.simps(3)
% 0.29/0.48 thf(fact_179_process__term_Oset__cases_I1_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,E: A,A2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ A2 ) )
% 0.29/0.48 => ( ! [Z3: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1062592052s_PROC @ A @ Pvar @ Z3 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z3 ) ) )
% 0.29/0.48 => ( ! [Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( A2
% 0.29/0.48 != ( proces1454156180ss_ACT @ A @ Pvar @ E @ Z2 ) )
% 0.29/0.48 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) )
% 0.29/0.48 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( A2
% 0.29/0.48 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z1 ) ) )
% 0.29/0.48 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.48 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.set_cases(1)
% 0.29/0.48 thf(fact_180_isACT_Oelims_I1_J,axiom,
% 0.29/0.48 ! [D: $tType,A: $tType,B: $tType,C: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 0.29/0.48 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 0.29/0.48 => ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.29/0.48 => ~ Y )
% 0.29/0.48 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.29/0.48 => Y ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.elims(1)
% 0.29/0.48 thf(fact_181_PREF_Oelims,axiom,
% 0.29/0.48 ! [A: $tType,C: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 0.29/0.48 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces460752237s_term @ C @ B @ B
% 0.29/0.48 @ ^ [Aa3: C] : ( undefined @ B )
% 0.29/0.48 @ ( proces745025900prefOf @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces745025900prefOf @ B @ P4 ) ) )
% 0.29/0.48 => ( ! [A4: B] :
% 0.29/0.48 ( ? [T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( Y != A4 ) )
% 0.29/0.48 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( undefined @ B ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.elims
% 0.29/0.48 thf(fact_182_CONT_Oelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 0.29/0.48 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( Y != T4 ) )
% 0.29/0.48 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.elims
% 0.29/0.48 thf(fact_183_process__term_Orel__cases,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B3: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B3 )
% 0.29/0.48 => ( ! [X3: Pvar] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
% 0.29/0.48 => ! [Y6: C] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces1627516585ss_VAR @ C @ B @ Y6 ) )
% 0.29/0.48 => ~ ( R22 @ X3 @ Y6 ) ) )
% 0.29/0.48 => ( ! [Xa2: proces634752977rocess @ A] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 0.29/0.48 => ! [Ya2: proces634752977rocess @ B] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ C @ Ya2 ) )
% 0.29/0.48 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya2 ) ) )
% 0.29/0.48 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 0.29/0.48 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 0.29/0.48 => ( ( R1 @ X1a @ Y1a )
% 0.29/0.48 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 0.29/0.48 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 0.29/0.48 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( B3
% 0.29/0.48 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 0.29/0.48 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 0.29/0.48 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_cases
% 0.29/0.48 thf(fact_184_process__term_Orel__induct,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X4: proces554692349s_term @ A @ Pvar,Y: proces554692349s_term @ B @ C,Q3: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X4 @ Y )
% 0.29/0.48 => ( ! [A12: Pvar,B1: C] :
% 0.29/0.48 ( ( R22 @ A12 @ B1 )
% 0.29/0.48 => ( Q3 @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 0.29/0.48 => ( ! [A23: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R1 @ A23 @ B22 )
% 0.29/0.48 => ( Q3 @ ( proces1062592052s_PROC @ A @ Pvar @ A23 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 0.29/0.48 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( R1 @ A31 @ B31 )
% 0.29/0.48 => ( ( Q3 @ A32 @ B32 )
% 0.29/0.48 => ( Q3 @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 0.29/0.48 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( Q3 @ A41 @ B41 )
% 0.29/0.48 => ( ( Q3 @ A42 @ B42 )
% 0.29/0.48 => ( Q3 @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 0.29/0.48 => ( Q3 @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_induct
% 0.29/0.48 thf(fact_185_isACT_Ocases,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) )
% 0.29/0.48 => ~ ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.cases
% 0.29/0.48 thf(fact_186_process__term_Orel__inject_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 0.29/0.48 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.29/0.48 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_inject(4)
% 0.29/0.48 thf(fact_187_process__term_Orel__inject_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 0.29/0.48 = ( ( R1 @ X31 @ Y31 )
% 0.29/0.48 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_inject(3)
% 0.29/0.48 thf(fact_188_process__term_Orel__intros_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.29/0.48 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 0.29/0.48 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_intros(4)
% 0.29/0.48 thf(fact_189_process__term_Orel__intros_I3_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 0.29/0.48 ( ( R1 @ X31 @ Y31 )
% 0.29/0.48 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 0.29/0.48 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_intros(3)
% 0.29/0.48 thf(fact_190_process__term_Orel__inject_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y13: C] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) )
% 0.29/0.48 = ( R22 @ X14 @ Y13 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_inject(1)
% 0.29/0.48 thf(fact_191_process__term_Orel__intros_I1_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X14: Pvar,Y13: C,R1: A > B > $o] :
% 0.29/0.48 ( ( R22 @ X14 @ Y13 )
% 0.29/0.48 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_intros(1)
% 0.29/0.48 thf(fact_192_process__term_Orel__refl,axiom,
% 0.29/0.48 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X4: proces554692349s_term @ C @ D] :
% 0.29/0.48 ( ! [X3: C] : ( R1a @ X3 @ X3 )
% 0.29/0.48 => ( ! [X3: D] : ( R2a @ X3 @ X3 )
% 0.29/0.48 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_refl
% 0.29/0.48 thf(fact_193_process__term_Orel__eq,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ A @ B @ B
% 0.29/0.48 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.29/0.48 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) )
% 0.29/0.48 = ( ^ [Y3: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y3 = Z ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_eq
% 0.29/0.48 thf(fact_194_process__term_Orel__map_I1_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1b: E2 > C > $o,S2b: F5 > D > $o,I1: A > E2,I2: B > F5,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D] :
% 0.29/0.48 ( ( proces2029722208s_term @ E2 @ C @ F5 @ D @ S1b @ S2b @ ( proces224683037s_term @ A @ E2 @ B @ F5 @ I1 @ I2 @ X4 ) @ Y )
% 0.29/0.48 = ( proces2029722208s_term @ A @ C @ B @ D
% 0.29/0.48 @ ^ [X: A] : ( S1b @ ( I1 @ X ) )
% 0.29/0.48 @ ^ [X: B] : ( S2b @ ( I2 @ X ) )
% 0.29/0.48 @ X4
% 0.29/0.48 @ Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_map(1)
% 0.29/0.48 thf(fact_195_process__term_Orel__map_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1a: A > E2 > $o,S2a: B > F5 > $o,X4: proces554692349s_term @ A @ B,G1: C > E2,G2: D > F5,Y: proces554692349s_term @ C @ D] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a @ X4 @ ( proces224683037s_term @ C @ E2 @ D @ F5 @ G1 @ G2 @ Y ) )
% 0.29/0.48 = ( proces2029722208s_term @ A @ C @ B @ D
% 0.29/0.48 @ ^ [X: A,Y4: C] : ( S1a @ X @ ( G1 @ Y4 ) )
% 0.29/0.48 @ ^ [X: B,Y4: D] : ( S2a @ X @ ( G2 @ Y4 ) )
% 0.29/0.48 @ X4
% 0.29/0.48 @ Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_map(2)
% 0.29/0.48 thf(fact_196_process__term_Orel__intros_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 0.29/0.48 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 0.29/0.48 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_intros(2)
% 0.29/0.48 thf(fact_197_process__term_Orel__inject_I2_J,axiom,
% 0.29/0.48 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 0.29/0.48 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 0.29/0.48 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_inject(2)
% 0.29/0.48 thf(fact_198_process__term_Orel__distinct_I2_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X14: D] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(2)
% 0.29/0.48 thf(fact_199_process__term_Orel__distinct_I1_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y2: proces634752977rocess @ B] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(1)
% 0.29/0.48 thf(fact_200_process__term_Orel__distinct_I10_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(10)
% 0.29/0.48 thf(fact_201_process__term_Orel__distinct_I9_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(9)
% 0.29/0.48 thf(fact_202_process__term_Orel__distinct_I8_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(8)
% 0.29/0.48 thf(fact_203_process__term_Orel__distinct_I7_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(7)
% 0.29/0.48 thf(fact_204_process__term_Orel__distinct_I6_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X14: D] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(6)
% 0.29/0.48 thf(fact_205_process__term_Orel__distinct_I5_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(5)
% 0.29/0.48 thf(fact_206_process__term_Orel__distinct_I4_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X14: D] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(4)
% 0.29/0.48 thf(fact_207_process__term_Orel__distinct_I3_J,axiom,
% 0.29/0.48 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(3)
% 0.29/0.48 thf(fact_208_process__term_Orel__distinct_I11_J,axiom,
% 0.29/0.48 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(11)
% 0.29/0.48 thf(fact_209_process__term_Orel__distinct_I12_J,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 0.29/0.48 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 0.29/0.48
% 0.29/0.48 % process_term.rel_distinct(12)
% 0.29/0.48 thf(fact_210_CH2_Ocases,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 0.29/0.48 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.cases
% 0.29/0.48 thf(fact_211_CONT_Ocases,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 0.29/0.48 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.cases
% 0.29/0.48 thf(fact_212_PREF_Ocases,axiom,
% 0.29/0.48 ! [C: $tType,A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.29/0.48 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.29/0.48 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 0.29/0.48 => ~ ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( X4
% 0.29/0.48 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.cases
% 0.29/0.48 thf(fact_213_CH1_Opelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.29/0.48 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( ( Y = T12 )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.29/0.48 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH1.pelims
% 0.29/0.48 thf(fact_214_CH2_Opelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.29/0.48 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( ( Y = T23 )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.29/0.48 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CH2.pelims
% 0.29/0.48 thf(fact_215_CONT_Opelims,axiom,
% 0.29/0.48 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.29/0.48 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.29/0.48 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( ( Y = T4 )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 0.29/0.48 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % CONT.pelims
% 0.29/0.48 thf(fact_216_PREF_Opelims,axiom,
% 0.29/0.48 ! [C: $tType,A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 0.29/0.48 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces460752237s_term @ C @ B @ B
% 0.29/0.48 @ ^ [Aa3: C] : ( undefined @ B )
% 0.29/0.48 @ ( proces745025900prefOf @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.29/0.48 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ B] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces745025900prefOf @ B @ P4 ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.29/0.48 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( ( Y = A4 )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 0.29/0.48 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( undefined @ B ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % PREF.pelims
% 0.29/0.48 thf(fact_217_isACT_Opelims_I1_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 0.29/0.48 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 = Y )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( ( Y
% 0.29/0.48 = ( proces10484146Action @ D @ P4 ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 0.29/0.48 => ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.29/0.48 => ( Y
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
% 0.29/0.48 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.29/0.48 => ( ~ Y
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.pelims(1)
% 0.29/0.48 thf(fact_218_isACT_Opelims_I3_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 0.29/0.48 => ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.29/0.48 => ( proces10484146Action @ D @ P4 ) ) )
% 0.29/0.48 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.pelims(3)
% 0.29/0.48 thf(fact_219_isACT_Opelims_I2_J,axiom,
% 0.29/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 0.29/0.48 => ( ! [X7: A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 0.29/0.48 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.29/0.48 @ ^ [Pvar2: C] : $false
% 0.29/0.48 @ ( proces10484146Action @ B )
% 0.29/0.48 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.29/0.48 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.29/0.48 @ ( X4 @ X7 ) ) ) )
% 0.29/0.48 => ( ! [P4: proces634752977rocess @ D] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.29/0.48 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.29/0.48 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 0.29/0.48 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.29/0.48 ( ( Xa
% 0.29/0.48 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.29/0.48 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % isACT.pelims(2)
% 0.29/0.48 thf(fact_220_pred__equals__eq2,axiom,
% 0.29/0.48 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.29/0.48 ( ( ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R ) )
% 0.29/0.48 = ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S ) ) )
% 0.29/0.49 = ( R = S ) ) ).
% 0.29/0.49
% 0.29/0.49 % pred_equals_eq2
% 0.29/0.49 thf(fact_221_process__term_Oset__cases_I2_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,E: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 0.29/0.49 => ( ( A2
% 0.29/0.49 != ( proces1627516585ss_VAR @ Pvar @ A @ E ) )
% 0.29/0.49 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( A2
% 0.29/0.49 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.49 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 0.29/0.49 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( A2
% 0.29/0.49 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.49 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 0.29/0.49 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( A2
% 0.29/0.49 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.29/0.49 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.set_cases(2)
% 0.29/0.49 thf(fact_222_process__term_Oset__intros_I6_J,axiom,
% 0.29/0.49 ! [A: $tType,Pvar: $tType,Ab2: Pvar] : ( member @ Pvar @ Ab2 @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.set_intros(6)
% 0.29/0.49 thf(fact_223_process__term_Oset__intros_I7_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 0.29/0.49 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 0.29/0.49 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.set_intros(7)
% 0.29/0.49 thf(fact_224_process__term_Oset__intros_I8_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 0.29/0.49 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.set_intros(8)
% 0.29/0.49 thf(fact_225_process__term_Oset__intros_I9_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 0.29/0.49 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.set_intros(9)
% 0.29/0.49 thf(fact_226_process__term_Osimps_I51_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.29/0.49 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.simps(51)
% 0.29/0.49 thf(fact_227_process__term_Orel__refl__strong,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.29/0.49 ( ! [Z1: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( R1a @ Z1 @ Z1 ) )
% 0.29/0.49 => ( ! [Z2: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( R2a @ Z2 @ Z2 ) )
% 0.29/0.49 => ( proces2029722208s_term @ A @ A @ B @ B @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.rel_refl_strong
% 0.29/0.49 thf(fact_228_process__term_Orel__mono__strong,axiom,
% 0.29/0.49 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.29/0.49 ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
% 0.29/0.49 => ( ! [Z1: A,Y1: C] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Y ) )
% 0.29/0.49 => ( ( R1 @ Z1 @ Y1 )
% 0.29/0.49 => ( R1a @ Z1 @ Y1 ) ) ) )
% 0.29/0.49 => ( ! [Z2: B,Y23: D] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Y ) )
% 0.29/0.49 => ( ( R22 @ Z2 @ Y23 )
% 0.29/0.49 => ( R2a @ Z2 @ Y23 ) ) ) )
% 0.29/0.49 => ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ X4 @ Y ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.rel_mono_strong
% 0.29/0.49 thf(fact_229_process__term_Orel__cong,axiom,
% 0.29/0.49 ! [A: $tType,B: $tType,D: $tType,C: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,Xa: proces554692349s_term @ C @ D,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 0.29/0.49 ( ( X4 = Ya )
% 0.29/0.49 => ( ( Y = Xa )
% 0.29/0.49 => ( ! [Z1: A,Y1: C] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Xa ) )
% 0.29/0.49 => ( ( R1 @ Z1 @ Y1 )
% 0.29/0.49 = ( R1a @ Z1 @ Y1 ) ) ) )
% 0.29/0.49 => ( ! [Z2: B,Y23: D] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Xa ) )
% 0.29/0.49 => ( ( R22 @ Z2 @ Y23 )
% 0.29/0.49 = ( R2a @ Z2 @ Y23 ) ) ) )
% 0.29/0.49 => ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
% 0.29/0.49 = ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.rel_cong
% 0.29/0.49 thf(fact_230_process__term_Omap__cong,axiom,
% 0.29/0.49 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.29/0.49 ( ( X4 = Ya )
% 0.29/0.49 => ( ! [Z1: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( F1 @ Z1 )
% 0.29/0.49 = ( G1 @ Z1 ) ) )
% 0.29/0.49 => ( ! [Z2: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( F2 @ Z2 )
% 0.29/0.49 = ( G2 @ Z2 ) ) )
% 0.29/0.49 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 0.29/0.49 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.map_cong
% 0.29/0.49 thf(fact_231_process__term_Omap__cong0,axiom,
% 0.29/0.49 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.29/0.49 ( ! [Z1: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( F1 @ Z1 )
% 0.29/0.49 = ( G1 @ Z1 ) ) )
% 0.29/0.49 => ( ! [Z2: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( F2 @ Z2 )
% 0.29/0.49 = ( G2 @ Z2 ) ) )
% 0.29/0.49 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 0.29/0.49 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ X4 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.map_cong0
% 0.29/0.49 thf(fact_232_process__term_Oinj__map__strong,axiom,
% 0.29/0.49 ! [C: $tType,D: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Xa: proces554692349s_term @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 0.29/0.49 ( ! [Z1: A,Z1a: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( member @ A @ Z1a @ ( proces1264666542s_term @ A @ B @ Xa ) )
% 0.29/0.49 => ( ( ( F1 @ Z1 )
% 0.29/0.49 = ( F1a @ Z1a ) )
% 0.29/0.49 => ( Z1 = Z1a ) ) ) )
% 0.29/0.49 => ( ! [Z2: B,Z2a: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( member @ B @ Z2a @ ( proces1493547885s_term @ A @ B @ Xa ) )
% 0.29/0.49 => ( ( ( F2 @ Z2 )
% 0.29/0.49 = ( F2a @ Z2a ) )
% 0.29/0.49 => ( Z2 = Z2a ) ) ) )
% 0.29/0.49 => ( ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 0.29/0.49 = ( proces224683037s_term @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 0.29/0.49 => ( X4 = Xa ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.inj_map_strong
% 0.29/0.49 thf(fact_233_process__term_Osimps_I49_J,axiom,
% 0.29/0.49 ! [A: $tType,Pvar: $tType,X14: Pvar] :
% 0.29/0.49 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 0.29/0.49 = ( insert @ Pvar @ X14 @ ( bot_bot @ ( set @ Pvar ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.simps(49)
% 0.29/0.49 thf(fact_234_process__term_Opred__mono__strong,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,X4: proces554692349s_term @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.29/0.49 ( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
% 0.29/0.49 => ( ! [Z1: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( P1 @ Z1 )
% 0.29/0.49 => ( P1a @ Z1 ) ) )
% 0.29/0.49 => ( ! [Z2: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 0.29/0.49 => ( ( P22 @ Z2 )
% 0.29/0.49 => ( P2a @ Z2 ) ) )
% 0.29/0.49 => ( proces2118920028s_term @ A @ B @ P1a @ P2a @ X4 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_mono_strong
% 0.29/0.49 thf(fact_235_singletonI,axiom,
% 0.29/0.49 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % singletonI
% 0.29/0.49 thf(fact_236_singleton__conv,axiom,
% 0.29/0.49 ! [A: $tType,A2: A] :
% 0.29/0.49 ( ( collect @ A
% 0.29/0.49 @ ^ [X: A] : ( X = A2 ) )
% 0.29/0.49 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % singleton_conv
% 0.29/0.49 thf(fact_237_singleton__conv2,axiom,
% 0.29/0.49 ! [A: $tType,A2: A] :
% 0.29/0.49 ( ( collect @ A
% 0.29/0.49 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.29/0.49 @ A2 ) )
% 0.29/0.49 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % singleton_conv2
% 0.29/0.49 thf(fact_238_process__term_Opred__inject_I1_J,axiom,
% 0.29/0.49 ! [A: $tType,Pvar: $tType,P1: A > $o,P22: Pvar > $o,A2: Pvar] :
% 0.29/0.49 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 0.29/0.49 = ( P22 @ A2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_inject(1)
% 0.29/0.49 thf(fact_239_process__term_Opred__inject_I4_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 0.29/0.49 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ A2 )
% 0.29/0.49 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_inject(4)
% 0.29/0.49 thf(fact_240_process__term_Opred__inject_I3_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.29/0.49 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 0.29/0.49 = ( ( P1 @ A2 )
% 0.29/0.49 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_inject(3)
% 0.29/0.49 thf(fact_241_process__term_Osimps_I50_J,axiom,
% 0.29/0.49 ! [A: $tType,Pvar: $tType,X2: proces634752977rocess @ A] :
% 0.29/0.49 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.29/0.49 = ( bot_bot @ ( set @ Pvar ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.simps(50)
% 0.29/0.49 thf(fact_242_process__term_Omap__cong__pred,axiom,
% 0.29/0.49 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.29/0.49 ( ( X4 = Ya )
% 0.29/0.49 => ( ( proces2118920028s_term @ A @ B
% 0.29/0.49 @ ^ [Z12: A] :
% 0.29/0.49 ( ( F1 @ Z12 )
% 0.29/0.49 = ( G1 @ Z12 ) )
% 0.29/0.49 @ ^ [Z22: B] :
% 0.29/0.49 ( ( F2 @ Z22 )
% 0.29/0.49 = ( G2 @ Z22 ) )
% 0.29/0.49 @ Ya )
% 0.29/0.49 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 0.29/0.49 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.map_cong_pred
% 0.29/0.49 thf(fact_243_process__term_Osimps_I45_J,axiom,
% 0.29/0.49 ! [Pvar: $tType,A: $tType,X14: Pvar] :
% 0.29/0.49 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 0.29/0.49 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.simps(45)
% 0.29/0.49 thf(fact_244_Collect__conv__if,axiom,
% 0.29/0.49 ! [A: $tType,P6: A > $o,A2: A] :
% 0.29/0.49 ( ( ( P6 @ A2 )
% 0.29/0.49 => ( ( collect @ A
% 0.29/0.49 @ ^ [X: A] :
% 0.29/0.49 ( ( X = A2 )
% 0.29/0.49 & ( P6 @ X ) ) )
% 0.29/0.49 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.49 & ( ~ ( P6 @ A2 )
% 0.29/0.49 => ( ( collect @ A
% 0.29/0.49 @ ^ [X: A] :
% 0.29/0.49 ( ( X = A2 )
% 0.29/0.49 & ( P6 @ X ) ) )
% 0.29/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Collect_conv_if
% 0.29/0.49 thf(fact_245_Collect__conv__if2,axiom,
% 0.29/0.49 ! [A: $tType,P6: A > $o,A2: A] :
% 0.29/0.49 ( ( ( P6 @ A2 )
% 0.29/0.49 => ( ( collect @ A
% 0.29/0.49 @ ^ [X: A] :
% 0.29/0.49 ( ( A2 = X )
% 0.29/0.49 & ( P6 @ X ) ) )
% 0.29/0.49 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.49 & ( ~ ( P6 @ A2 )
% 0.29/0.49 => ( ( collect @ A
% 0.29/0.49 @ ^ [X: A] :
% 0.29/0.49 ( ( A2 = X )
% 0.29/0.49 & ( P6 @ X ) ) )
% 0.29/0.49 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Collect_conv_if2
% 0.29/0.49 thf(fact_246_process__term_Opred__True,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType] :
% 0.29/0.49 ( ( proces2118920028s_term @ A @ B
% 0.29/0.49 @ ^ [Uu: A] : $true
% 0.29/0.49 @ ^ [Uu: B] : $true )
% 0.29/0.49 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_True
% 0.29/0.49 thf(fact_247_empty__def,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( bot_bot @ ( set @ A ) )
% 0.29/0.49 = ( collect @ A
% 0.29/0.49 @ ^ [X: A] : $false ) ) ).
% 0.29/0.49
% 0.29/0.49 % empty_def
% 0.29/0.49 thf(fact_248_singleton__inject,axiom,
% 0.29/0.49 ! [A: $tType,A2: A,B3: A] :
% 0.29/0.49 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.29/0.49 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.49 => ( A2 = B3 ) ) ).
% 0.29/0.49
% 0.29/0.49 % singleton_inject
% 0.29/0.49 thf(fact_249_insert__not__empty,axiom,
% 0.29/0.49 ! [A: $tType,A2: A,A6: set @ A] :
% 0.29/0.49 ( ( insert @ A @ A2 @ A6 )
% 0.29/0.49 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % insert_not_empty
% 0.29/0.49 thf(fact_250_doubleton__eq__iff,axiom,
% 0.29/0.49 ! [A: $tType,A2: A,B3: A,C3: A,D2: A] :
% 0.29/0.49 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.49 = ( insert @ A @ C3 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.49 = ( ( ( A2 = C3 )
% 0.29/0.49 & ( B3 = D2 ) )
% 0.29/0.49 | ( ( A2 = D2 )
% 0.29/0.49 & ( B3 = C3 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % doubleton_eq_iff
% 0.29/0.49 thf(fact_251_singleton__iff,axiom,
% 0.29/0.49 ! [A: $tType,B3: A,A2: A] :
% 0.29/0.49 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.49 = ( B3 = A2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % singleton_iff
% 0.29/0.49 thf(fact_252_singletonD,axiom,
% 0.29/0.49 ! [A: $tType,B3: A,A2: A] :
% 0.29/0.49 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.49 => ( B3 = A2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % singletonD
% 0.29/0.49 thf(fact_253_process__term_Opred__cong,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 0.29/0.49 ( ( X4 = Ya )
% 0.29/0.49 => ( ! [Z1: A] :
% 0.29/0.49 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( P1 @ Z1 )
% 0.29/0.49 = ( P1a @ Z1 ) ) )
% 0.29/0.49 => ( ! [Z2: B] :
% 0.29/0.49 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 0.29/0.49 => ( ( P22 @ Z2 )
% 0.29/0.49 = ( P2a @ Z2 ) ) )
% 0.29/0.49 => ( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
% 0.29/0.49 = ( proces2118920028s_term @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % process_term.pred_cong
% 0.29/0.49 thf(fact_254_the__elem__eq,axiom,
% 0.29/0.49 ! [A: $tType,X4: A] :
% 0.29/0.49 ( ( the_elem @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.49 = X4 ) ).
% 0.29/0.49
% 0.29/0.49 % the_elem_eq
% 0.29/0.49
% 0.29/0.49 %----Helper facts (3)
% 0.29/0.49 thf(help_If_3_1_T,axiom,
% 0.29/0.49 ! [P6: $o] :
% 0.29/0.49 ( ( P6 = $true )
% 0.29/0.49 | ( P6 = $false ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(help_If_2_1_T,axiom,
% 0.29/0.49 ! [A: $tType,X4: A,Y: A] :
% 0.29/0.49 ( ( if @ A @ $false @ X4 @ Y )
% 0.29/0.49 = Y ) ).
% 0.29/0.49
% 0.29/0.49 thf(help_If_1_1_T,axiom,
% 0.29/0.49 ! [A: $tType,X4: A,Y: A] :
% 0.29/0.49 ( ( if @ A @ $true @ X4 @ Y )
% 0.29/0.49 = X4 ) ).
% 0.29/0.49
% 0.29/0.49 %----Conjectures (1)
% 0.29/0.49 thf(conj_0,conjecture,
% 0.29/0.49 ( ( ( proces10484146Action @ a @ pa )
% 0.29/0.49 = ( proces10484146Action @ a @ p2 ) )
% 0.29/0.49 & ( ( proces401113213Choice @ a @ pa )
% 0.29/0.49 = ( proces401113213Choice @ a @ p2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 3.06/1.67 ---- Embedded in THF ---
% 3.06/1.67 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.06/1.67 %%% Generated on Tue Feb 24 11:29:43 EST 2026
% 3.06/1.67 %%% using '$$dhol' embedding, version 1.3.0.
% 3.06/1.67 %%% Logic specification used:
% 3.06/1.67 %%% thf(spec, logic, $$dhol).
% 3.06/1.67
% 3.06/1.67 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2DTF1352.p
% 3.06/1.67 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term, type, proces554692349s_term: ($tType > ($tType > $tType))).
% 3.06/1.67 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess, type, proces634752977rocess: ($tType > $tType)).
% 3.06/1.67 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.06/1.67 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.06/1.67 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.06/1.67 thf(ty_tf_b, type, b: $tType).
% 3.06/1.67 thf(ty_tf_a, type, a: $tType).
% 3.06/1.67 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 3.06/1.67 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.06/1.67 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1, type, proces1239275103le_CH1: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel, type, proces1869379930H1_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2, type, proces1239275104le_CH2: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel, type, proces93903513H2_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT, type, proces126235999e_CONT: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel, type, proces1004198490NT_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF, type, proces1708129104e_PREF: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > B))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel, type, proces527360425EF_rel: (!> [A:$tType,B:$tType,C:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded, type, proces1121166967uarded: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > $o)))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT, type, proces687458811_isACT: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel, type, proces896239806CT_rel: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > $o))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction, type, proces1525233512Action: (!> [A:$tType]: ((A > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice, type, proces1915862579Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process, type, proces1406508781rocess: (!> [A:$tType,B:$tType]: (((A > ((proces634752977rocess @ A) > B)) > (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)) > ((proces634752977rocess @ A) > B)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of, type, proces979765041_ch1Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of, type, proces988026546_ch2Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf, type, proces1778668539contOf: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process, type, proces894737309rocess: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction, type, proces10484146Action: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice, type, proces401113213Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process, type, proces370407749rocess: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((proces634752977rocess @ A) > (proces634752977rocess @ Aa)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf, type, proces745025900prefOf: (!> [A:$tType]: (((proces634752977rocess @ A) > A)))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process, type, proces749077512rocess: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process, type, proces1148692671rocess: (!> [A:$tType]: (((proces634752977rocess @ A) > (set @ A))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT, type, proces1454156180ss_ACT: (!> [A:$tType,Pvar:$tType]: ((A > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH, type, proces89589571ess_CH: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC, type, proces1062592052s_PROC: (!> [A:$tType,Pvar:$tType]: (((proces634752977rocess @ A) > ((proces554692349s_term @ A) @ Pvar))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR, type, proces1627516585ss_VAR: (!> [Pvar:$tType,A:$tType]: ((Pvar > ((proces554692349s_term @ A) @ Pvar))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term, type, proces460752237s_term: (!> [Pvar:$tType,B:$tType,A:$tType]: (((Pvar > B) > (((proces634752977rocess @ A) > B) > ((A > (((proces554692349s_term @ A) @ Pvar) > B)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)) > (((proces554692349s_term @ A) @ Pvar) > B)))))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term, type, proces224683037s_term: (!> [A:$tType,Aa:$tType,Pvar:$tType,Pvara:$tType]: (((A > Aa) > ((Pvar > Pvara) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ Aa) @ Pvara))))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term, type, proces2118920028s_term: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((proces554692349s_term @ A) @ B) > $o)))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term, type, proces2029722208s_term: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset1__process__term, type, proces1264666542s_term: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (set @ A))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term, type, proces1493547885s_term: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (set @ Pvar))))).
% 3.06/1.67 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution, type, proces1652378886lution: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > (proces634752977rocess @ B)))))).
% 3.06/1.67 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.06/1.67 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 3.06/1.67 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.06/1.67 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.06/1.67 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.06/1.67 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 3.06/1.67 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.06/1.67 thf(sy_v_p, type, p: (proces634752977rocess @ a)).
% 3.06/1.67 thf(sy_v_p_H____, type, p2: (proces634752977rocess @ a)).
% 3.06/1.67 thf(sy_v_pa____, type, pa: (proces634752977rocess @ a)).
% 3.06/1.67 thf(sy_v_q____, type, q: (proces634752977rocess @ a)).
% 3.06/1.67 thf(sy_v_sys, type, sys: (b > ((proces554692349s_term @ a) @ b))).
% 3.06/1.67 thf(fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062, axiom, (((proces10484146Action @ a) @ pa) | ((proces401113213Choice @ a) @ pa))).
% 3.06/1.67 thf(fact_1_process_Odistinct__disc_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => (~ (((proces10484146Action @ A) @ Process))))))).
% 3.06/1.67 thf(fact_2_process_Odistinct__disc_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => (~ (((proces401113213Choice @ A) @ Process))))))).
% 3.06/1.67 thf(fact_3_isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ P) | ((proces401113213Choice @ A) @ P))))).
% 3.06/1.67 thf(fact_4_process_Oexhaust__disc, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((~ (((proces10484146Action @ A) @ Process))) => ((proces401113213Choice @ A) @ Process))))).
% 3.06/1.67 thf(fact_5_not__isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((~ ((((proces10484146Action @ A) @ P) & ((proces401113213Choice @ A) @ P))))))).
% 3.06/1.67 thf(fact_6_process_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (~ ((P @ A2))))))).
% 3.06/1.67 thf(fact_7_process_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (P @ A2))))).
% 3.06/1.67 thf(fact_8_iss, axiom, (p2 = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ pa)))).
% 3.06/1.67 thf(fact_9_process_Omap__disc__iff_I2_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces401113213Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces401113213Choice @ A) @ A2))))).
% 3.06/1.67 thf(fact_10_process_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => ((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 3.06/1.67 thf(fact_11_process_Omap__disc__iff_I1_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces10484146Action @ A) @ A2))))).
% 3.06/1.67 thf(fact_12_process_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => ((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 3.06/1.67 thf(fact_13_process_Odisc_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((proces401113213Choice @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22))))).
% 3.06/1.67 thf(fact_14_process_Odisc_I3_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((~ (((proces401113213Choice @ A) @ (((proces1525233512Action @ A) @ X11) @ X12))))))).
% 3.06/1.67 thf(fact_15_process_OdiscI_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((Process = (((proces1915862579Choice @ A) @ X21) @ X22)) => ((proces401113213Choice @ A) @ Process))))).
% 3.06/1.67 thf(fact_16_isChoice__def, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X212:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((Process2 = (((proces1915862579Choice @ A) @ X212) @ X222)))))))))).
% 3.06/1.67 thf(fact_17_process_Odisc_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((~ (((proces10484146Action @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22))))))).
% 3.06/1.67 thf(fact_18_process__term_Oinject_I2_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ A)]: ((((((proces1062592052s_PROC @ A) @ Pvar) @ X2) = (((proces1062592052s_PROC @ A) @ Pvar) @ Y2)) = (X2 = Y2))))).
% 3.06/1.67 thf(fact_19_process_Oinject_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A),Y11:A,Y12:(proces634752977rocess @ A)]: ((((((proces1525233512Action @ A) @ X11) @ X12) = (((proces1525233512Action @ A) @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 3.06/1.67 thf(fact_20_process_Oinject_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A)]: ((((((proces1915862579Choice @ A) @ X21) @ X22) = (((proces1915862579Choice @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 3.06/1.67 thf(fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062, axiom, (q = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ p)))).
% 3.06/1.67 thf(fact_22_process_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q21 @ A2)) @ (G211 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q22 @ A2)) @ (G221 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 3.06/1.67 thf(fact_23_process_Ocorec_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1525233512Action @ A) @ (G11 @ A2)) @ ((((if @ (proces634752977rocess @ A)) @ (Q12 @ A2)) @ (G121 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 3.06/1.67 thf(fact_24_process_Osimps_I16_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = (((proces1915862579Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ X21)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X22)))))).
% 3.06/1.67 thf(fact_25_process_Osimps_I15_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X11:A,X12:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1525233512Action @ A) @ X11) @ X12)) = (((proces1525233512Action @ B) @ (F @ X11)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X12)))))).
% 3.06/1.67 thf(fact_26_process_Odistinct_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((((proces1525233512Action @ A) @ X11) @ X12) != (((proces1915862579Choice @ A) @ X21) @ X22))))).
% 3.06/1.67 thf(fact_27_process_Oexhaust, axiom, (! [A:$tType,Y:(proces634752977rocess @ A)]: (((! [X112:A,X122:(proces634752977rocess @ A)]: ((Y != (((proces1525233512Action @ A) @ X112) @ X122)))) => (~ ((! [X213:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((Y != (((proces1915862579Choice @ A) @ X213) @ X223)))))))))).
% 3.06/1.67 thf(fact_28_process_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((proces894737309rocess @ C) @ A) = (^ [P2:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A3:C]: (((((if @ (proces634752977rocess @ A)) @ (P2 @ A3)) @ (((proces1525233512Action @ A) @ (G112 @ A3)) @ ((((if @ (proces634752977rocess @ A)) @ (Q122 @ A3)) @ (G1212 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P2) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A3))))) @ (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q212 @ A3)) @ (G2112 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P2) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A3)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q222 @ A3)) @ (G2212 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P2) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A3))))))))))).
% 3.06/1.67 thf(fact_29_process_Omap__ident, axiom, (! [A:$tType,T:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ A) @ (^ [X:A]: (X))) @ T) = T)))).
% 3.06/1.67 thf(fact_30_process__strong__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P3:(proces634752977rocess @ A)]: ((((Phi @ P) @ P3) => ((! [P4:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P5) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P5)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P5)))))) => ((! [A4:A,A5:A,P4:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A4) @ P4)) @ (((proces1525233512Action @ A) @ A5) @ P5)) => ((A4 = A5) & (((Phi @ P4) @ P5) | (P4 = P5)))))) => ((! [P4:(proces634752977rocess @ A),Q:(proces634752977rocess @ A),P5:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q)) @ (((proces1915862579Choice @ A) @ P5) @ Q2)) => ((((Phi @ P4) @ P5) | (P4 = P5)) & (((Phi @ Q) @ Q2) | (Q = Q2)))))) => (P = P3)))))))).
% 3.06/1.67 thf(fact_31_process__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P3:(proces634752977rocess @ A)]: ((((Phi @ P) @ P3) => ((! [P4:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P5) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P5)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P5)))))) => ((! [A4:A,A5:A,P4:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A4) @ P4)) @ (((proces1525233512Action @ A) @ A5) @ P5)) => ((A4 = A5) & ((Phi @ P4) @ P5))))) => ((! [P4:(proces634752977rocess @ A),Q:(proces634752977rocess @ A),P5:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q)) @ (((proces1915862579Choice @ A) @ P5) @ Q2)) => (((Phi @ P4) @ P5) & ((Phi @ Q) @ Q2))))) => (P = P3)))))))).
% 3.06/1.67 thf(fact_32_isAction__def, axiom, (! [A:$tType]: (((proces10484146Action @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X113:A,X123:(proces634752977rocess @ A)]: ((Process2 = (((proces1525233512Action @ A) @ X113) @ X123)))))))))).
% 3.06/1.67 thf(fact_33_process_OdiscI_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X11:A,X12:(proces634752977rocess @ A)]: (((Process = (((proces1525233512Action @ A) @ X11) @ X12)) => ((proces10484146Action @ A) @ Process))))).
% 3.06/1.67 thf(fact_34_process_Odisc_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: (((proces10484146Action @ A) @ (((proces1525233512Action @ A) @ X11) @ X12))))).
% 3.06/1.67 thf(fact_35_solution_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))))).
% 3.06/1.67 thf(fact_36_solution_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))).
% 3.06/1.67 thf(fact_37_solution_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => ((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.06/1.67 thf(fact_38_solution_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => ((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.06/1.67 thf(fact_39_process_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces10484146Action @ A) @ A2) => (((proces745025900prefOf @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = (F @ ((proces745025900prefOf @ A) @ A2))))))).
% 3.06/1.67 thf(fact_40_process_Omap__sel_I3_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces979765041_ch1Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces979765041_ch1Of @ A) @ A2))))))).
% 3.06/1.67 thf(fact_41_process_Omap__sel_I4_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces988026546_ch2Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces988026546_ch2Of @ A) @ A2))))))).
% 3.06/1.67 thf(fact_42_isACT_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ D)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1062592052s_PROC @ D) @ A) @ P)) = ((proces10484146Action @ D) @ P))))).
% 3.06/1.67 thf(fact_43_process_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces10484146Action @ A) @ A2) => (((proces1778668539contOf @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces1778668539contOf @ A) @ A2))))))).
% 3.06/1.67 thf(fact_44_process_Odisc__eq__case_I2_J, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ($false))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ($true))))))).
% 3.06/1.67 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P6:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P6)) = (P6 @ A2))))).
% 3.06/1.67 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A6:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A6)))) = A6)))).
% 3.06/1.67 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P6:(A > $o),Q3:(A > $o)]: (((! [X3:A]: (((P6 @ X3) = (Q3 @ X3)))) => (((collect @ A) @ P6) = ((collect @ A) @ Q3)))))).
% 3.06/1.67 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 3.06/1.67 thf(fact_49_process_Ocollapse_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => ((((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)) = Process))))).
% 3.06/1.67 thf(fact_50_process_Ocollapse_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => ((((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process)) = Process))))).
% 3.06/1.67 thf(fact_51_process_Osplit__sel, axiom, (! [B:$tType,A:$tType,P6:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P6 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (P6 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))) & ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) => (P6 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))).
% 3.06/1.67 thf(fact_52_process_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((proces1406508781rocess @ A) @ B) = (^ [F12:(A > ((proces634752977rocess @ A) > B)),F22:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process2:(proces634752977rocess @ A)]: (((((if @ B) @ ((proces10484146Action @ A) @ Process2)) @ ((F12 @ ((proces745025900prefOf @ A) @ Process2)) @ ((proces1778668539contOf @ A) @ Process2))) @ ((F22 @ ((proces979765041_ch1Of @ A) @ Process2)) @ ((proces988026546_ch2Of @ A) @ Process2))))))))).
% 3.06/1.67 thf(fact_53_process_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P6:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P6 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (~ ((((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) & (~ ((P6 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))))) | ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) & (~ ((P6 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))))))).
% 3.06/1.67 thf(fact_54_process_Oexhaust__sel, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((Process != (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))).
% 3.06/1.67 thf(fact_55_process_Oexpand, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: (((((proces10484146Action @ A) @ Process) = ((proces10484146Action @ A) @ Process3)) => ((((proces10484146Action @ A) @ Process) => (((proces10484146Action @ A) @ Process3) => ((((proces745025900prefOf @ A) @ Process) = ((proces745025900prefOf @ A) @ Process3)) & (((proces1778668539contOf @ A) @ Process) = ((proces1778668539contOf @ A) @ Process3))))) => ((((proces401113213Choice @ A) @ Process) => (((proces401113213Choice @ A) @ Process3) => ((((proces979765041_ch1Of @ A) @ Process) = ((proces979765041_ch1Of @ A) @ Process3)) & (((proces988026546_ch2Of @ A) @ Process) = ((proces988026546_ch2Of @ A) @ Process3))))) => (Process = Process3))))))).
% 3.06/1.67 thf(fact_56_process_Ocoinduct, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & ((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => (((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) & ((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)))))))))) => (Process = Process3)))))).
% 3.06/1.67 thf(fact_57_process_Ocoinduct__strong, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & (((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5)) | (((proces1778668539contOf @ A) @ Process4) = ((proces1778668539contOf @ A) @ Process5)))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => ((((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) | (((proces979765041_ch1Of @ A) @ Process4) = ((proces979765041_ch1Of @ A) @ Process5))) & (((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)) | (((proces988026546_ch2Of @ A) @ Process4) = ((proces988026546_ch2Of @ A) @ Process5))))))))))) => (Process = Process3)))))).
% 3.06/1.67 thf(fact_58_process_Ocase__distrib, axiom, (! [B:$tType,C:$tType,A:$tType,H:(B > C),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((H @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((((proces1406508781rocess @ A) @ C) @ (^ [X1:A,X23:(proces634752977rocess @ A)]: ((H @ ((F1 @ X1) @ X23))))) @ (^ [X1:(proces634752977rocess @ A),X23:(proces634752977rocess @ A)]: ((H @ ((F2 @ X1) @ X23))))) @ Process))))).
% 3.06/1.67 thf(fact_59_process_Osel_I2_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces1778668539contOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = X12)))).
% 3.06/1.67 thf(fact_60_process_Osel_I3_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((proces979765041_ch1Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = X21)))).
% 3.06/1.67 thf(fact_61_process_Osel_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((proces988026546_ch2Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = X22)))).
% 3.06/1.67 thf(fact_62_process_Osel_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces745025900prefOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = X11)))).
% 3.06/1.67 thf(fact_63_process_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q12:(C > $o),G11:(C > A),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((Q12 @ A2) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G121 @ A2))) & ((~ ((Q12 @ A2))) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 3.06/1.67 thf(fact_64_process_Ocorec__sel_I3_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q21:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q21 @ A2) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G211 @ A2))) & ((~ ((Q21 @ A2))) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2))))))))).
% 3.06/1.67 thf(fact_65_process_Ocorec__sel_I4_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q22:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q22 @ A2) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G221 @ A2))) & ((~ ((Q22 @ A2))) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 3.06/1.67 thf(fact_66_process_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((proces745025900prefOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G11 @ A2)))))).
% 3.06/1.67 thf(fact_67_process_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X11:A,X12:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1525233512Action @ A) @ X11) @ X12)) = ((F1 @ X11) @ X12))))).
% 3.06/1.67 thf(fact_68_process_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 3.06/1.67 thf(fact_69_process_Odisc__eq__case_I1_J, axiom, (! [A:$tType]: (((proces10484146Action @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ($true))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ($false))))))).
% 3.06/1.67 thf(fact_70_solution_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces745025900prefOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)))))).
% 3.06/1.67 thf(fact_71_solution_Osimps_I5_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces979765041_ch1Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))))))).
% 3.06/1.67 thf(fact_72_solution_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces988026546_ch2Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2))))))).
% 3.06/1.67 thf(fact_73_solution_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces1778668539contOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2))))))).
% 3.06/1.67 thf(fact_74_process_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P6:((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)),X4:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),R:(A > (B > $o))]: ((((P6 @ X4) @ Y) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ B)]: ((((P6 @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ B) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ B) @ Process5) => (((R @ ((proces745025900prefOf @ A) @ Process4)) @ ((proces745025900prefOf @ B) @ Process5)) & ((P6 @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ B) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ B) @ Process5) => (((P6 @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ B) @ Process5)) & ((P6 @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ B) @ Process5)))))))))) => (((((proces749077512rocess @ A) @ B) @ R) @ X4) @ Y)))))).
% 3.06/1.67 thf(fact_75_process_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((proces749077512rocess @ A) @ B) = (^ [R2:(A > (B > $o)),A3:(proces634752977rocess @ A),B2:(proces634752977rocess @ B)]: (((((proces10484146Action @ A) @ A3) = ((proces10484146Action @ B) @ B2)) & ((((proces10484146Action @ A) @ A3) => (((proces10484146Action @ B) @ B2) => (((R2 @ ((proces745025900prefOf @ A) @ A3)) @ ((proces745025900prefOf @ B) @ B2)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces1778668539contOf @ A) @ A3)) @ ((proces1778668539contOf @ B) @ B2))))) & (((proces401113213Choice @ A) @ A3) => (((proces401113213Choice @ B) @ B2) => ((((((proces749077512rocess @ A) @ B) @ R2) @ ((proces979765041_ch1Of @ A) @ A3)) @ ((proces979765041_ch1Of @ B) @ B2)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces988026546_ch2Of @ A) @ A3)) @ ((proces988026546_ch2Of @ B) @ B2))))))))))))).
% 3.06/1.67 thf(fact_76_PREF_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ B)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = ((proces745025900prefOf @ B) @ P))))).
% 3.06/1.67 thf(fact_77_CH2_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P)))))).
% 3.06/1.67 thf(fact_78_process_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X12:(proces634752977rocess @ A),Y11:B,Y12:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1525233512Action @ B) @ Y11) @ Y12)) = (((R @ X11) @ Y11) & (((((proces749077512rocess @ A) @ B) @ R) @ X12) @ Y12)))))).
% 3.06/1.67 thf(fact_79_process_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X22)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22)) = ((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) & (((((proces749077512rocess @ A) @ B) @ R) @ X22) @ Y22)))))).
% 3.06/1.67 thf(fact_80_process_Orel__eq, axiom, (! [A:$tType]: (((((proces749077512rocess @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) = (^ [Y3:(proces634752977rocess @ A),Z:(proces634752977rocess @ A)]: ((Y3 = Z))))))).
% 3.06/1.67 thf(fact_81_process_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X4:(proces634752977rocess @ B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => (((((proces749077512rocess @ B) @ B) @ Ra) @ X4) @ X4))))).
% 3.06/1.67 thf(fact_82_process_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,Y11:B,X12:(proces634752977rocess @ A),Y12:(proces634752977rocess @ B)]: ((((R @ X11) @ Y11) => ((((((proces749077512rocess @ A) @ B) @ R) @ X12) @ Y12) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1525233512Action @ B) @ Y11) @ Y12))))))).
% 3.06/1.67 thf(fact_83_process_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),X22:(proces634752977rocess @ A),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) => ((((((proces749077512rocess @ A) @ B) @ R) @ X22) @ Y22) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X22)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.06/1.67 thf(fact_84_process_Orel__map_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sa:(A > (C > $o)),X4:(proces634752977rocess @ A),G:(B > C),Y:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ C) @ Sa) @ X4) @ ((((proces370407749rocess @ B) @ C) @ G) @ Y)) = (((((proces749077512rocess @ A) @ B) @ (^ [X:A,Y4:B]: (((Sa @ X) @ (G @ Y4))))) @ X4) @ Y))))).
% 3.06/1.67 thf(fact_85_process_Orel__map_I1_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sb:(C > (B > $o)),I:(A > C),X4:(proces634752977rocess @ A),Y:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ C) @ B) @ Sb) @ ((((proces370407749rocess @ A) @ C) @ I) @ X4)) @ Y) = (((((proces749077512rocess @ A) @ B) @ (^ [X:A]: ((Sb @ (I @ X))))) @ X4) @ Y))))).
% 3.06/1.67 thf(fact_86_solution_Ocode, axiom, (! [B:$tType,A:$tType]: ((((proces1652378886lution @ A) @ B) = (^ [Sys2:(A > ((proces554692349s_term @ B) @ A)),T3:((proces554692349s_term @ B) @ A)]: (((((if @ (proces634752977rocess @ B)) @ ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys2) @ T3)) @ (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys2) @ T3)) @ ((((proces1652378886lution @ A) @ B) @ Sys2) @ ((((proces126235999e_CONT @ A) @ B) @ Sys2) @ T3)))) @ (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys2) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys2) @ T3))) @ ((((proces1652378886lution @ A) @ B) @ Sys2) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys2) @ T3)))))))))).
% 3.06/1.67 thf(fact_87_process_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A),X11:B,X12:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ Y21) @ Y22)) @ (((proces1525233512Action @ B) @ X11) @ X12))))))).
% 3.06/1.67 thf(fact_88_process_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X12:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.06/1.67 thf(fact_89_process_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(proces634752977rocess @ A),B3:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ A2) @ B3) => ((! [X13:A,X24:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ X13) @ X24)) => (! [Y1:B,Y23:(proces634752977rocess @ B)]: (((B3 = (((proces1525233512Action @ B) @ Y1) @ Y23)) => (((R @ X13) @ Y1) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X24) @ Y23)))))))))) => (~ ((! [X1a:(proces634752977rocess @ A),X2a:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ X1a) @ X2a)) => (! [Y1a:(proces634752977rocess @ B),Y2a:(proces634752977rocess @ B)]: (((B3 = (((proces1915862579Choice @ B) @ Y1a) @ Y2a)) => ((((((proces749077512rocess @ A) @ B) @ R) @ X1a) @ Y1a) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X2a) @ Y2a))))))))))))))))).
% 3.06/1.67 thf(fact_90_solution_Octr_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2)))))))).
% 3.06/1.67 thf(fact_91_solution_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2)))))))).
% 3.06/1.67 thf(fact_92_CONT_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P)))))).
% 3.06/1.67 thf(fact_93_CH1_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P)))))).
% 3.06/1.67 thf(fact_94_prefOf__def, axiom, (! [A:$tType]: (((proces745025900prefOf @ A) = ((((proces1406508781rocess @ A) @ A) @ (^ [X113:A,X123:(proces634752977rocess @ A)]: (X113))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ((undefined @ A)))))))).
% 3.06/1.67 thf(fact_95_process_Oset__sel_I3_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),Xa:A]: ((((proces401113213Choice @ A) @ A2) => ((((member @ A) @ Xa) @ ((proces1148692671rocess @ A) @ ((proces979765041_ch1Of @ A) @ A2))) => (((member @ A) @ Xa) @ ((proces1148692671rocess @ A) @ A2))))))).
% 3.06/1.67 thf(fact_96_process_Oset__sel_I4_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),Xb:A]: ((((proces401113213Choice @ A) @ A2) => ((((member @ A) @ Xb) @ ((proces1148692671rocess @ A) @ ((proces988026546_ch2Of @ A) @ A2))) => (((member @ A) @ Xb) @ ((proces1148692671rocess @ A) @ A2))))))).
% 3.06/1.67 thf(fact_97_process_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ A2) => (((member @ A) @ ((proces745025900prefOf @ A) @ A2)) @ ((proces1148692671rocess @ A) @ A2)))))).
% 3.06/1.67 thf(fact_98_process_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),X4:A]: ((((proces10484146Action @ A) @ A2) => ((((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ ((proces1778668539contOf @ A) @ A2))) => (((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ A2))))))).
% 3.06/1.67 thf(fact_99_process_Oset__cases, axiom, (! [A:$tType,E:A,A2:(proces634752977rocess @ A)]: (((((member @ A) @ E) @ ((proces1148692671rocess @ A) @ A2)) => ((! [Z2:(proces634752977rocess @ A)]: ((A2 != (((proces1525233512Action @ A) @ E) @ Z2)))) => ((! [Z1:A,Z2:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((proces1148692671rocess @ A) @ Z2))))))) => ((! [Z1:(proces634752977rocess @ A)]: (((? [Z2:(proces634752977rocess @ A)]: ((A2 = (((proces1915862579Choice @ A) @ Z1) @ Z2)))) => (~ ((((member @ A) @ E) @ ((proces1148692671rocess @ A) @ Z1))))))) => (~ ((! [Z1:(proces634752977rocess @ A),Z2:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((proces1148692671rocess @ A) @ Z2)))))))))))))))).
% 3.06/1.67 thf(fact_100_process_Orel__refl__strong, axiom, (! [A:$tType,X4:(proces634752977rocess @ A),Ra:(A > (A > $o))]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ X4)) => ((Ra @ Z3) @ Z3)))) => (((((proces749077512rocess @ A) @ A) @ Ra) @ X4) @ X4))))).
% 3.06/1.67 thf(fact_101_process_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X4:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),Ra:(A > (B > $o))]: (((((((proces749077512rocess @ A) @ B) @ R) @ X4) @ Y) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ X4)) => ((((member @ B) @ Yb) @ ((proces1148692671rocess @ B) @ Y)) => (((R @ Z3) @ Yb) => ((Ra @ Z3) @ Yb)))))) => (((((proces749077512rocess @ A) @ B) @ Ra) @ X4) @ Y)))))).
% 3.06/1.67 thf(fact_102_process_Orel__cong, axiom, (! [A:$tType,B:$tType,X4:(proces634752977rocess @ A),Ya:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),Xa:(proces634752977rocess @ B),R:(A > (B > $o)),Ra:(A > (B > $o))]: (((X4 = Ya) => ((Y = Xa) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((proces1148692671rocess @ B) @ Xa)) => (((R @ Z3) @ Yb) = ((Ra @ Z3) @ Yb)))))) => ((((((proces749077512rocess @ A) @ B) @ R) @ X4) @ Y) = (((((proces749077512rocess @ A) @ B) @ Ra) @ Ya) @ Xa)))))))).
% 3.06/1.67 thf(fact_103_process_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(proces634752977rocess @ A)]: ((((member @ A) @ A1) @ ((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ A1) @ A22)))))).
% 3.06/1.67 thf(fact_104_process_Oset__intros_I2_J, axiom, (! [A:$tType,X4:A,A22:(proces634752977rocess @ A),A1:A]: (((((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ A22)) => (((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ A1) @ A22))))))).
% 3.06/1.67 thf(fact_105_process_Oset__intros_I3_J, axiom, (! [A:$tType,Xa:A,A1a:(proces634752977rocess @ A),A2a:(proces634752977rocess @ A)]: (((((member @ A) @ Xa) @ ((proces1148692671rocess @ A) @ A1a)) => (((member @ A) @ Xa) @ ((proces1148692671rocess @ A) @ (((proces1915862579Choice @ A) @ A1a) @ A2a))))))).
% 3.06/1.67 thf(fact_106_process_Oset__intros_I4_J, axiom, (! [A:$tType,Xb:A,A2a:(proces634752977rocess @ A),A1a:(proces634752977rocess @ A)]: (((((member @ A) @ Xb) @ ((proces1148692671rocess @ A) @ A2a)) => (((member @ A) @ Xb) @ ((proces1148692671rocess @ A) @ (((proces1915862579Choice @ A) @ A1a) @ A2a))))))).
% 3.06/1.67 thf(fact_107_process_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X4:(proces634752977rocess @ A),Xa:(proces634752977rocess @ A),F:(A > B),Fa:(A > B)]: (((! [Z3:A,Za:A]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ X4)) => ((((member @ A) @ Za) @ ((proces1148692671rocess @ A) @ Xa)) => (((F @ Z3) = (Fa @ Za)) => (Z3 = Za)))))) => ((((((proces370407749rocess @ A) @ B) @ F) @ X4) = ((((proces370407749rocess @ A) @ B) @ Fa) @ Xa)) => (X4 = Xa)))))).
% 3.06/1.67 thf(fact_108_process_Omap__cong0, axiom, (! [B:$tType,A:$tType,X4:(proces634752977rocess @ A),F:(A > B),G:(A > B)]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ X4)) => ((F @ Z3) = (G @ Z3))))) => (((((proces370407749rocess @ A) @ B) @ F) @ X4) = ((((proces370407749rocess @ A) @ B) @ G) @ X4)))))).
% 3.06/1.67 thf(fact_109_process_Omap__cong, axiom, (! [B:$tType,A:$tType,X4:(proces634752977rocess @ A),Ya:(proces634752977rocess @ A),F:(A > B),G:(A > B)]: (((X4 = Ya) => ((! [Z3:A]: (((((member @ A) @ Z3) @ ((proces1148692671rocess @ A) @ Ya)) => ((F @ Z3) = (G @ Z3))))) => (((((proces370407749rocess @ A) @ B) @ F) @ X4) = ((((proces370407749rocess @ A) @ B) @ G) @ Ya))))))).
% 3.06/1.67 thf(fact_110_contOf__def, axiom, (! [A:$tType]: (((proces1778668539contOf @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [X113:A,X123:(proces634752977rocess @ A)]: (X123))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))))))).
% 3.06/1.67 thf(fact_111_ch1Of__def, axiom, (! [A:$tType]: (((proces979765041_ch1Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X212:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X212))))))).
% 3.06/1.67 thf(fact_112_ch2Of__def, axiom, (! [A:$tType]: (((proces988026546_ch2Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X212:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X222))))))).
% 3.06/1.67 thf(fact_113_process_Oset__induct, axiom, (! [A:$tType,X4:A,A2:(proces634752977rocess @ A),P6:(A > ((proces634752977rocess @ A) > $o))]: (((((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ A2)) => ((! [Z1:A,Z2:(proces634752977rocess @ A)]: (((P6 @ Z1) @ (((proces1525233512Action @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(proces634752977rocess @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((proces1148692671rocess @ A) @ Z2)) => (((P6 @ Xa2) @ Z2) => ((P6 @ Xa2) @ (((proces1525233512Action @ A) @ Z1) @ Z2)))))) => ((! [Z1a:(proces634752977rocess @ A),Z2a:(proces634752977rocess @ A),Xb2:A]: (((((member @ A) @ Xb2) @ ((proces1148692671rocess @ A) @ Z1a)) => (((P6 @ Xb2) @ Z1a) => ((P6 @ Xb2) @ (((proces1915862579Choice @ A) @ Z1a) @ Z2a)))))) => ((! [Z1a:(proces634752977rocess @ A),Z2a:(proces634752977rocess @ A),Xc:A]: (((((member @ A) @ Xc) @ ((proces1148692671rocess @ A) @ Z2a)) => (((P6 @ Xc) @ Z2a) => ((P6 @ Xc) @ (((proces1915862579Choice @ A) @ Z1a) @ Z2a)))))) => ((P6 @ X4) @ A2))))))))).
% 3.06/1.67 thf(fact_114_process_Osimps_I21_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = (((insert @ A) @ X11) @ ((proces1148692671rocess @ A) @ X12)))))).
% 3.06/1.67 thf(fact_115_process__term_Osimps_I46_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A)]: (((((proces1264666542s_term @ A) @ Pvar) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = ((proces1148692671rocess @ A) @ X2))))).
% 3.06/1.67 thf(fact_116_process__term_Oset__intros_I1_J, axiom, (! [Pvar:$tType,A:$tType,X4:A,Aa2:(proces634752977rocess @ A)]: (((((member @ A) @ X4) @ ((proces1148692671rocess @ A) @ Aa2)) => (((member @ A) @ X4) @ (((proces1264666542s_term @ A) @ Pvar) @ (((proces1062592052s_PROC @ A) @ Pvar) @ Aa2))))))).
% 3.06/1.67 thf(fact_117_process__term_Osimps_I26_J, axiom, (! [Pvar:$tType,C:$tType,B:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X2:(proces634752977rocess @ A)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (((proces1062592052s_PROC @ B) @ C) @ ((((proces370407749rocess @ A) @ B) @ F1) @ X2)))))).
% 3.06/1.67 thf(fact_118_PREF_Osimps_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X5:A]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X5)) = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (Sys @ X5)))))).
% 3.06/1.67 thf(fact_119_process__term_Oinject_I1_J, axiom, (! [A:$tType,Pvar:$tType,X14:Pvar,Y13:Pvar]: ((((((proces1627516585ss_VAR @ Pvar) @ A) @ X14) = (((proces1627516585ss_VAR @ Pvar) @ A) @ Y13)) = (X14 = Y13))))).
% 3.06/1.67 thf(fact_120_process__term_Ocase__distrib, axiom, (! [B:$tType,C:$tType,Pvar:$tType,A:$tType,H:(B > C),F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((H @ ((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ Process_term)) = ((((((((proces460752237s_term @ Pvar) @ C) @ A) @ (^ [X:Pvar]: ((H @ (F1 @ X))))) @ (^ [X:(proces634752977rocess @ A)]: ((H @ (F2 @ X))))) @ (^ [X1:A,X23:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F3 @ X1) @ X23))))) @ (^ [X1:((proces554692349s_term @ A) @ Pvar),X23:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F4 @ X1) @ X23))))) @ Process_term))))).
% 3.06/1.67 thf(fact_121_process__term_Omap__ident, axiom, (! [B:$tType,A:$tType,T:((proces554692349s_term @ A) @ B)]: (((((((((proces224683037s_term @ A) @ A) @ B) @ B) @ (^ [X:A]: (X))) @ (^ [X:B]: (X))) @ T) = T)))).
% 3.06/1.67 thf(fact_122_process__term_Osimps_I25_J, axiom, (! [A:$tType,B:$tType,C:$tType,Pvar:$tType,F1:(A > B),F2:(Pvar > C),X14:Pvar]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) = (((proces1627516585ss_VAR @ C) @ B) @ (F2 @ X14)))))).
% 3.06/1.67 thf(fact_123_process__term_Osimps_I17_J, axiom, (! [A:$tType,B:$tType,Pvar:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X14:Pvar]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) = (F1 @ X14))))).
% 3.06/1.67 thf(fact_124_process__term_Odistinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,X14:Pvar,X2:(proces634752977rocess @ A)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X14) != (((proces1062592052s_PROC @ A) @ Pvar) @ X2))))).
% 3.06/1.67 thf(fact_125_isACT_Osimps_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X5:A]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1627516585ss_VAR @ A) @ D) @ X5)) = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (Sys @ X5)))))).
% 3.06/1.67 thf(fact_126_process__term_Osimps_I18_J, axiom, (! [Pvar:$tType,B:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X2:(proces634752977rocess @ A)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 3.06/1.67 thf(fact_127_CONT_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X5:A]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X5)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P2))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (Sys @ X5)))))).
% 3.06/1.67 thf(fact_128_CH2_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X5:A]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X5)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T22))) @ (Sys @ X5)))))).
% 3.06/1.67 thf(fact_129_CH1_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X5:A]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X5)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T1))) @ (Sys @ X5)))))).
% 3.06/1.67 thf(fact_130_insertCI, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: ((((~ ((((member @ A) @ A2) @ B4))) => (A2 = B3)) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 3.06/1.67 thf(fact_131_insert__iff, axiom, (! [A:$tType,A2:A,B3:A,A6:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A6)) = ((A2 = B3) | (((member @ A) @ A2) @ A6)))))).
% 3.06/1.67 thf(fact_132_insert__absorb2, axiom, (! [A:$tType,X4:A,A6:(set @ A)]: (((((insert @ A) @ X4) @ (((insert @ A) @ X4) @ A6)) = (((insert @ A) @ X4) @ A6))))).
% 3.06/1.67 thf(fact_133_solution__VAR, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X5:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((proces1652378886lution @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X5)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ (Sys @ X5))))))).
% 3.06/1.67 thf(fact_134_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ A6) => (? [B5:(set @ A)]: (((A6 = (((insert @ A) @ A2) @ B5)) & (~ ((((member @ A) @ A2) @ B5)))))))))).
% 3.06/1.67 thf(fact_135_insert__commute, axiom, (! [A:$tType,X4:A,Y:A,A6:(set @ A)]: (((((insert @ A) @ X4) @ (((insert @ A) @ Y) @ A6)) = (((insert @ A) @ Y) @ (((insert @ A) @ X4) @ A6)))))).
% 3.06/1.67 thf(fact_136_insert__eq__iff, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:A,B4:(set @ A)]: (((~ ((((member @ A) @ A2) @ A6))) => ((~ ((((member @ A) @ B3) @ B4))) => (((((insert @ A) @ A2) @ A6) = (((insert @ A) @ B3) @ B4)) = (((A2 = B3) => (A6 = B4)) & ((A2 != B3) => (? [C2:(set @ A)]: (((A6 = (((insert @ A) @ B3) @ C2)) & ((~ ((((member @ A) @ B3) @ C2))) & ((B4 = (((insert @ A) @ A2) @ C2)) & (~ ((((member @ A) @ A2) @ C2)))))))))))))))).
% 3.06/1.67 thf(fact_137_insert__absorb, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ A6) => ((((insert @ A) @ A2) @ A6) = A6))))).
% 3.06/1.67 thf(fact_138_insert__ident, axiom, (! [A:$tType,X4:A,A6:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X4) @ A6))) => ((~ ((((member @ A) @ X4) @ B4))) => (((((insert @ A) @ X4) @ A6) = (((insert @ A) @ X4) @ B4)) = (A6 = B4))))))).
% 3.06/1.67 thf(fact_139_Set_Oset__insert, axiom, (! [A:$tType,X4:A,A6:(set @ A)]: (((((member @ A) @ X4) @ A6) => (~ ((! [B5:(set @ A)]: (((A6 = (((insert @ A) @ X4) @ B5)) => (((member @ A) @ X4) @ B5)))))))))).
% 3.06/1.67 thf(fact_140_insertI2, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: (((((member @ A) @ A2) @ B4) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 3.06/1.67 thf(fact_141_insertI1, axiom, (! [A:$tType,A2:A,B4:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B4))))).
% 3.06/1.67 thf(fact_142_insertE, axiom, (! [A:$tType,A2:A,B3:A,A6:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A6)) => ((A2 != B3) => (((member @ A) @ A2) @ A6)))))).
% 3.06/1.67 thf(fact_143_guarded__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((proces1121166967uarded @ A) @ B) @ C) = (^ [Sys2:(A > ((proces554692349s_term @ B) @ C))]: ((! [X6:A,Y5:C]: (((Sys2 @ X6) != (((proces1627516585ss_VAR @ C) @ B) @ Y5)))))))))).
% 3.06/1.67 thf(fact_144_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A3:A,B6:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((X = A3) | (((member @ A) @ X) @ B6))))))))))).
% 3.06/1.67 thf(fact_145_insert__Collect, axiom, (! [A:$tType,A2:A,P6:(A > $o)]: (((((insert @ A) @ A2) @ ((collect @ A) @ P6)) = ((collect @ A) @ (^ [U:A]: (((U != A2) => (P6 @ U))))))))).
% 3.06/1.67 thf(fact_146_isACT__VAR, axiom, (! [C:$tType,B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X5:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((((proces687458811_isACT @ A) @ B) @ A) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ C) @ X5)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ (Sys @ X5))))))).
% 3.06/1.67 thf(fact_147_isACT_Oelims_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (~ (((proces10484146Action @ D) @ P4)))))) => (~ ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))))))))))).
% 3.06/1.67 thf(fact_148_isACT_Oelims_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa))) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((proces10484146Action @ D) @ P4)))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))))))))))).
% 3.06/1.67 thf(fact_149_CH2_Oelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X4) @ Xa) = Y) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T22))) @ (X4 @ X7)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => (Y != T23)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.06/1.67 thf(fact_150_CH1_Oelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X4) @ Xa) = Y) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T1))) @ (X4 @ X7)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A)]: (((? [T23:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => (Y != T12)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.06/1.67 thf(fact_151_process__term_Oinject_I4_J, axiom, (! [Pvar:$tType,A:$tType,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ A) @ Pvar)]: (((((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42) = ((((proces89589571ess_CH @ A) @ Pvar) @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 3.06/1.67 thf(fact_152_process__term_Oinject_I3_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:A,Y32:((proces554692349s_term @ A) @ Pvar)]: (((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 3.06/1.67 thf(fact_153_process__term_Osimps_I47_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1264666542s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((insert @ A) @ X31) @ (((proces1264666542s_term @ A) @ Pvar) @ X32)))))).
% 3.06/1.67 thf(fact_154_process__term_Osimps_I20_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((F4 @ X41) @ X42))))).
% 3.06/1.67 thf(fact_155_isACT_Osimps_I4_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),T13:((proces554692349s_term @ D) @ A),T24:((proces554692349s_term @ D) @ A)]: ((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces89589571ess_CH @ D) @ A) @ T13) @ T24))))))).
% 3.06/1.67 thf(fact_156_process__term_Osimps_I19_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((F3 @ X31) @ X32))))).
% 3.06/1.67 thf(fact_157_isACT_Osimps_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:D,T2:((proces554692349s_term @ D) @ A)]: (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces1454156180ss_ACT @ D) @ A) @ A2) @ T2))))).
% 3.06/1.67 thf(fact_158_process__term_Odistinct_I11_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.06/1.67 thf(fact_159_process__term_Odistinct_I7_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.06/1.67 thf(fact_160_process__term_Odistinct_I9_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.06/1.67 thf(fact_161_process__term_Oset__intros_I2_J, axiom, (! [Pvar:$tType,A:$tType,A1:A,A22:((proces554692349s_term @ A) @ Pvar)]: ((((member @ A) @ A1) @ (((proces1264666542s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1) @ A22)))))).
% 3.06/1.67 thf(fact_162_process__term_Oset__intros_I3_J, axiom, (! [Pvar:$tType,A:$tType,Xa:A,A22:((proces554692349s_term @ A) @ Pvar),A1:A]: (((((member @ A) @ Xa) @ (((proces1264666542s_term @ A) @ Pvar) @ A22)) => (((member @ A) @ Xa) @ (((proces1264666542s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1) @ A22))))))).
% 3.06/1.67 thf(fact_163_process__term_Oset__intros_I4_J, axiom, (! [Pvar:$tType,A:$tType,Xc2:A,A1a:((proces554692349s_term @ A) @ Pvar),A2a:((proces554692349s_term @ A) @ Pvar)]: (((((member @ A) @ Xc2) @ (((proces1264666542s_term @ A) @ Pvar) @ A1a)) => (((member @ A) @ Xc2) @ (((proces1264666542s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1a) @ A2a))))))).
% 3.06/1.67 thf(fact_164_process__term_Oset__intros_I5_J, axiom, (! [Pvar:$tType,A:$tType,Xe:A,A2a:((proces554692349s_term @ A) @ Pvar),A1a:((proces554692349s_term @ A) @ Pvar)]: (((((member @ A) @ Xe) @ (((proces1264666542s_term @ A) @ Pvar) @ A2a)) => (((member @ A) @ Xe) @ (((proces1264666542s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1a) @ A2a))))))).
% 3.06/1.67 thf(fact_165_process__term_Odistinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,X14:Pvar,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X14) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.06/1.67 thf(fact_166_process__term_Odistinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,X14:Pvar,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X14) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.06/1.67 thf(fact_167_process__term_Osimps_I27_J, axiom, (! [C:$tType,B:$tType,Pvar:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((((proces1454156180ss_ACT @ B) @ C) @ (F1 @ X31)) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X32)))))).
% 3.06/1.67 thf(fact_168_process__term_Osimps_I28_J, axiom, (! [C:$tType,B:$tType,Pvar:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((((proces89589571ess_CH @ B) @ C) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X41)) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X42)))))).
% 3.06/1.67 thf(fact_169_process__term_Oexhaust, axiom, (! [Pvar:$tType,A:$tType,Y:((proces554692349s_term @ A) @ Pvar)]: (((! [X13:Pvar]: ((Y != (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)))) => ((! [X24:(proces634752977rocess @ A)]: ((Y != (((proces1062592052s_PROC @ A) @ Pvar) @ X24)))) => ((! [X312:A,X322:((proces554692349s_term @ A) @ Pvar)]: ((Y != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X312) @ X322)))) => (~ ((! [X412:((proces554692349s_term @ A) @ Pvar),X422:((proces554692349s_term @ A) @ Pvar)]: ((Y != ((((proces89589571ess_CH @ A) @ Pvar) @ X412) @ X422)))))))))))).
% 3.06/1.67 thf(fact_170_process__term_Oinduct, axiom, (! [Pvar:$tType,A:$tType,P6:(((proces554692349s_term @ A) @ Pvar) > $o),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((! [X3:Pvar]: ((P6 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X3)))) => ((! [X3:(proces634752977rocess @ A)]: ((P6 @ (((proces1062592052s_PROC @ A) @ Pvar) @ X3)))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((P6 @ X2a) => (P6 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a))))) => ((! [X1a:((proces554692349s_term @ A) @ Pvar),X2a:((proces554692349s_term @ A) @ Pvar)]: (((P6 @ X1a) => ((P6 @ X2a) => (P6 @ ((((proces89589571ess_CH @ A) @ Pvar) @ X1a) @ X2a)))))) => (P6 @ Process_term)))))))).
% 3.06/1.67 thf(fact_171_isACT_Oinduct, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,P6:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ D) @ A)]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),X7:A]: (((P6 @ Sys3) @ (((proces1627516585ss_VAR @ A) @ D) @ X7)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: (((P6 @ Sys3) @ (((proces1062592052s_PROC @ D) @ A) @ P4)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),A4:D,T4:((proces554692349s_term @ D) @ A)]: (((P6 @ Sys3) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((P6 @ Sys3) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => ((P6 @ A0) @ A1)))))))).
% 3.06/1.67 thf(fact_172_PREF_Oinduct, axiom, (! [C:$tType,A:$tType,B:$tType,P6:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),X7:A]: (((P6 @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: (((P6 @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),A4:B,T4:((proces554692349s_term @ B) @ A)]: (((P6 @ Sys3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P6 @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P6 @ A0) @ A1)))))))).
% 3.06/1.67 thf(fact_173_CONT_Oinduct, axiom, (! [A:$tType,B:$tType,P6:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),X7:A]: (((P6 @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P6 @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),A4:B,T4:((proces554692349s_term @ B) @ A)]: (((P6 @ Sys3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P6 @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P6 @ A0) @ A1)))))))).
% 3.06/1.67 thf(fact_174_CH2_Oinduct, axiom, (! [A:$tType,B:$tType,P6:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),X7:A]: (((P6 @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P6 @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((P6 @ Sys3) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: (((P6 @ A4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => ((P6 @ A0) @ A1)))))))).
% 3.06/1.67 thf(fact_175_CH1_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T13) @ T24)) = T13)))).
% 3.06/1.67 thf(fact_176_CH2_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T13) @ T24)) = T24)))).
% 3.06/1.67 thf(fact_177_CONT_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),A2:B,T2:((proces554692349s_term @ B) @ A)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = T2)))).
% 3.06/1.67 thf(fact_178_PREF_Osimps_I3_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:B,T2:((proces554692349s_term @ B) @ A)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = A2)))).
% 3.06/1.67 thf(fact_179_process__term_Oset__cases_I1_J, axiom, (! [Pvar:$tType,A:$tType,E:A,A2:((proces554692349s_term @ A) @ Pvar)]: (((((member @ A) @ E) @ (((proces1264666542s_term @ A) @ Pvar) @ A2)) => ((! [Z3:(proces634752977rocess @ A)]: (((A2 = (((proces1062592052s_PROC @ A) @ Pvar) @ Z3)) => (~ ((((member @ A) @ E) @ ((proces1148692671rocess @ A) @ Z3))))))) => ((! [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 != ((((proces1454156180ss_ACT @ A) @ Pvar) @ E) @ Z2)))) => ((! [Z1:A,Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ (((proces1264666542s_term @ A) @ Pvar) @ Z2))))))) => ((! [Z1:((proces554692349s_term @ A) @ Pvar)]: (((? [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)))) => (~ ((((member @ A) @ E) @ (((proces1264666542s_term @ A) @ Pvar) @ Z1))))))) => (~ ((! [Z1:((proces554692349s_term @ A) @ Pvar),Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ (((proces1264666542s_term @ A) @ Pvar) @ Z2))))))))))))))))).
% 3.06/1.67 thf(fact_180_isACT_Oelims_I1_J, axiom, (! [D:$tType,A:$tType,B:$tType,C:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa) = Y) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => (Y = (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (Y = (~ (((proces10484146Action @ D) @ P4))))))) => (((? [A4:D,T4:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))) => (~ (Y))) => (~ (((? [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => Y)))))))))).
% 3.06/1.67 thf(fact_181_PREF_Oelims, axiom, (! [A:$tType,C:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X4) @ Xa) = Y) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => (Y != ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X4 @ X7)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y != ((proces745025900prefOf @ B) @ P4))))) => ((! [A4:B]: (((? [T4:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => (Y != A4)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ B)))))))))))).
% 3.06/1.67 thf(fact_182_CONT_Oelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X4) @ Xa) = Y) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P2))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X4 @ X7)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4)))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => (Y != T4)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.06/1.67 thf(fact_183_process__term_Orel__cases, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),A2:((proces554692349s_term @ A) @ Pvar),B3:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ A2) @ B3) => ((! [X3:Pvar]: (((A2 = (((proces1627516585ss_VAR @ Pvar) @ A) @ X3)) => (! [Y6:C]: (((B3 = (((proces1627516585ss_VAR @ C) @ B) @ Y6)) => (~ (((R22 @ X3) @ Y6))))))))) => ((! [Xa2:(proces634752977rocess @ A)]: (((A2 = (((proces1062592052s_PROC @ A) @ Pvar) @ Xa2)) => (! [Ya2:(proces634752977rocess @ B)]: (((B3 = (((proces1062592052s_PROC @ B) @ C) @ Ya2)) => (~ ((((((proces749077512rocess @ A) @ B) @ R1) @ Xa2) @ Ya2))))))))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a)) => (! [Y1a:B,Y2a:((proces554692349s_term @ B) @ C)]: (((B3 = ((((proces1454156180ss_ACT @ B) @ C) @ Y1a) @ Y2a)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2a) @ Y2a)))))))))) => (~ ((! [X1b:((proces554692349s_term @ A) @ Pvar),X2b:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ X1b) @ X2b)) => (! [Y1b:((proces554692349s_term @ B) @ C),Y2b:((proces554692349s_term @ B) @ C)]: (((B3 = ((((proces89589571ess_CH @ B) @ C) @ Y1b) @ Y2b)) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X1b) @ Y1b) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2b) @ Y2b))))))))))))))))))).
% 3.06/1.67 thf(fact_184_process__term_Orel__induct, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X4:((proces554692349s_term @ A) @ Pvar),Y:((proces554692349s_term @ B) @ C),Q3:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ B) @ C) > $o))]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X4) @ Y) => ((! [A12:Pvar,B1:C]: ((((R22 @ A12) @ B1) => ((Q3 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A12)) @ (((proces1627516585ss_VAR @ C) @ B) @ B1))))) => ((! [A23:(proces634752977rocess @ A),B22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R1) @ A23) @ B22) => ((Q3 @ (((proces1062592052s_PROC @ A) @ Pvar) @ A23)) @ (((proces1062592052s_PROC @ B) @ C) @ B22))))) => ((! [A31:A,A32:((proces554692349s_term @ A) @ Pvar),B31:B,B32:((proces554692349s_term @ B) @ C)]: ((((R1 @ A31) @ B31) => (((Q3 @ A32) @ B32) => ((Q3 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A31) @ A32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ B31) @ B32)))))) => ((! [A41:((proces554692349s_term @ A) @ Pvar),A42:((proces554692349s_term @ A) @ Pvar),B41:((proces554692349s_term @ B) @ C),B42:((proces554692349s_term @ B) @ C)]: ((((Q3 @ A41) @ B41) => (((Q3 @ A42) @ B42) => ((Q3 @ ((((proces89589571ess_CH @ A) @ Pvar) @ A41) @ A42)) @ ((((proces89589571ess_CH @ B) @ C) @ B41) @ B42)))))) => ((Q3 @ X4) @ Y))))))))).
% 3.06/1.67 thf(fact_185_isACT_Ocases, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X4:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),X7:A]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys3) @ (((proces1627516585ss_VAR @ A) @ D) @ X7))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys3) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),A4:D,T4:((proces554692349s_term @ D) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys3) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))) => (~ ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys3) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))).
% 3.06/1.67 thf(fact_186_process__term_Orel__inject_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42)) = (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42)))))).
% 3.06/1.67 thf(fact_187_process__term_Orel__inject_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32)) = (((R1 @ X31) @ Y31) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32)))))).
% 3.06/1.67 thf(fact_188_process__term_Orel__intros_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),X42:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.06/1.67 thf(fact_189_process__term_Orel__intros_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X31:A,Y31:B,R22:(Pvar > (C > $o)),X32:((proces554692349s_term @ A) @ Pvar),Y32:((proces554692349s_term @ B) @ C)]: ((((R1 @ X31) @ Y31) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.06/1.67 thf(fact_190_process__term_Orel__inject_I1_J, axiom, (! [B:$tType,A:$tType,Pvar:$tType,C:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X14:Pvar,Y13:C]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y13)) = ((R22 @ X14) @ Y13))))).
% 3.06/1.67 thf(fact_191_process__term_Orel__intros_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),X14:Pvar,Y13:C,R1:(A > (B > $o))]: ((((R22 @ X14) @ Y13) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y13)))))).
% 3.06/1.67 thf(fact_192_process__term_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X4:((proces554692349s_term @ C) @ D)]: (((! [X3:C]: (((R1a @ X3) @ X3))) => ((! [X3:D]: (((R2a @ X3) @ X3))) => ((((((((proces2029722208s_term @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X4) @ X4)))))).
% 3.06/1.67 thf(fact_193_process__term_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((proces2029722208s_term @ A) @ A) @ B) @ B) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))) = (^ [Y3:((proces554692349s_term @ A) @ B),Z:((proces554692349s_term @ A) @ B)]: ((Y3 = Z))))))).
% 3.06/1.67 thf(fact_194_process__term_Orel__map_I1_J, axiom, (! [A:$tType,B:$tType,E2:$tType,F5:$tType,D:$tType,C:$tType,S1b:(E2 > (C > $o)),S2b:(F5 > (D > $o)),I1:(A > E2),I2:(B > F5),X4:((proces554692349s_term @ A) @ B),Y:((proces554692349s_term @ C) @ D)]: ((((((((((proces2029722208s_term @ E2) @ C) @ F5) @ D) @ S1b) @ S2b) @ (((((((proces224683037s_term @ A) @ E2) @ B) @ F5) @ I1) @ I2) @ X4)) @ Y) = ((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ (^ [X:A]: ((S1b @ (I1 @ X))))) @ (^ [X:B]: ((S2b @ (I2 @ X))))) @ X4) @ Y))))).
% 3.06/1.67 thf(fact_195_process__term_Orel__map_I2_J, axiom, (! [A:$tType,B:$tType,E2:$tType,F5:$tType,D:$tType,C:$tType,S1a:(A > (E2 > $o)),S2a:(B > (F5 > $o)),X4:((proces554692349s_term @ A) @ B),G1:(C > E2),G2:(D > F5),Y:((proces554692349s_term @ C) @ D)]: ((((((((((proces2029722208s_term @ A) @ E2) @ B) @ F5) @ S1a) @ S2a) @ X4) @ (((((((proces224683037s_term @ C) @ E2) @ D) @ F5) @ G1) @ G2) @ Y)) = ((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ (^ [X:A,Y4:C]: (((S1a @ X) @ (G1 @ Y4))))) @ (^ [X:B,Y4:D]: (((S2a @ X) @ (G2 @ Y4))))) @ X4) @ Y))))).
% 3.06/1.67 thf(fact_196_process__term_Orel__intros_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B),R22:(Pvar > (C > $o))]: (((((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)))))).
% 3.06/1.67 thf(fact_197_process__term_Orel__inject_I2_J, axiom, (! [C:$tType,Pvar:$tType,A:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)) = (((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2))))).
% 3.06/1.67 thf(fact_198_process__term_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y2:(proces634752977rocess @ A),X14:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ B) @ Y2)) @ (((proces1627516585ss_VAR @ D) @ C) @ X14))))))).
% 3.06/1.67 thf(fact_199_process__term_Orel__distinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X14:Pvar,Y2:(proces634752977rocess @ B)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2))))))).
% 3.06/1.67 thf(fact_200_process__term_Orel__distinct_I10_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.06/1.67 thf(fact_201_process__term_Orel__distinct_I9_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.06/1.67 thf(fact_202_process__term_Orel__distinct_I8_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.06/1.67 thf(fact_203_process__term_Orel__distinct_I7_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.06/1.67 thf(fact_204_process__term_Orel__distinct_I6_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X14:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1627516585ss_VAR @ D) @ C) @ X14))))))).
% 3.06/1.67 thf(fact_205_process__term_Orel__distinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X14:Pvar,Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.06/1.67 thf(fact_206_process__term_Orel__distinct_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X14:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1627516585ss_VAR @ D) @ C) @ X14))))))).
% 3.06/1.67 thf(fact_207_process__term_Orel__distinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X14:Pvar,Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.06/1.67 thf(fact_208_process__term_Orel__distinct_I11_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.06/1.67 thf(fact_209_process__term_Orel__distinct_I12_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X31:C,X32:((proces554692349s_term @ C) @ D)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ ((((proces1454156180ss_ACT @ C) @ D) @ X31) @ X32))))))).
% 3.06/1.67 thf(fact_210_CH2_Ocases, axiom, (! [A:$tType,B:$tType,X4:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),X7:A]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))).
% 3.06/1.67 thf(fact_211_CONT_Ocases, axiom, (! [A:$tType,B:$tType,X4:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),X7:A]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ A)),A4:B,T4:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.06/1.67 thf(fact_212_PREF_Ocases, axiom, (! [C:$tType,A:$tType,B:$tType,X4:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),X7:A]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys3:(A > ((proces554692349s_term @ B) @ C)),A4:B,T4:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X4 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.06/1.67 thf(fact_213_CH1_Opelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X4) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T1))) @ (X4 @ X7))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y = T12) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.06/1.67 thf(fact_214_CH2_Opelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X4) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P2))))) @ (^ [A3:B,B2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: (T22))) @ (X4 @ X7))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y = T23) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.06/1.67 thf(fact_215_CONT_Opelims, axiom, (! [A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X4) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P2:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P2))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X4 @ X7))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => ((Y = T4) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.06/1.67 thf(fact_216_PREF_Opelims, axiom, (! [C:$tType,A:$tType,B:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X4) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X7)) => ((Y = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X4 @ X7))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ B) @ X7))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y = ((proces745025900prefOf @ B) @ P4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => ((Y = A4) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ B)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.06/1.67 thf(fact_217_isACT_Opelims_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => ((Y = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ D) @ X7))))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((Y = ((proces10484146Action @ D) @ P4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))))))) => ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)) => (Y => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => ((~ (Y)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))))).
% 3.06/1.67 thf(fact_218_isACT_Opelims_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa))) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ D) @ X7))) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7)))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => ((proces10484146Action @ D) @ P4))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))).
% 3.06/1.67 thf(fact_219_isACT_Opelims_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X4:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X4) @ Xa) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ Xa)) => ((! [X7:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X7)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1627516585ss_VAR @ A) @ D) @ X7))) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X4 @ X7)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => (~ (((proces10484146Action @ D) @ P4))))))) => (~ ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X4) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))))))))))))))).
% 3.06/1.67 thf(fact_220_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X:A,Y4:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ R))) = (^ [X:A,Y4:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ S)))) = (R = S))))).
% 3.06/1.67 thf(fact_221_process__term_Oset__cases_I2_J, axiom, (! [Pvar:$tType,A:$tType,E:Pvar,A2:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ A2)) => ((A2 != (((proces1627516585ss_VAR @ Pvar) @ A) @ E)) => ((! [Z1:A,Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2))))))) => ((! [Z1:((proces554692349s_term @ A) @ Pvar)]: (((? [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)))) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z1))))))) => (~ ((! [Z1:((proces554692349s_term @ A) @ Pvar),Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2)))))))))))))))).
% 3.06/1.67 thf(fact_222_process__term_Oset__intros_I6_J, axiom, (! [A:$tType,Pvar:$tType,Ab2:Pvar]: ((((member @ Pvar) @ Ab2) @ (((proces1493547885s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ Ab2)))))).
% 3.06/1.67 thf(fact_223_process__term_Oset__intros_I7_J, axiom, (! [Pvar:$tType,A:$tType,Xi:Pvar,A2b:((proces554692349s_term @ A) @ Pvar),A1b:A]: (((((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ A2b)) => (((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1b) @ A2b))))))).
% 3.06/1.67 thf(fact_224_process__term_Oset__intros_I8_J, axiom, (! [Pvar:$tType,A:$tType,Xk:Pvar,A1c:((proces554692349s_term @ A) @ Pvar),A2c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ A1c)) => (((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.06/1.67 thf(fact_225_process__term_Oset__intros_I9_J, axiom, (! [Pvar:$tType,A:$tType,Xm:Pvar,A2c:((proces554692349s_term @ A) @ Pvar),A1c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ A2c)) => (((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.06/1.67 thf(fact_226_process__term_Osimps_I51_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((proces1493547885s_term @ A) @ Pvar) @ X32))))).
% 3.06/1.67 thf(fact_227_process__term_Orel__refl__strong, axiom, (! [B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),R1a:(A > (A > $o)),R2a:(B > (B > $o))]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ X4)) => ((R1a @ Z1) @ Z1)))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ X4)) => ((R2a @ Z2) @ Z2)))) => ((((((((proces2029722208s_term @ A) @ A) @ B) @ B) @ R1a) @ R2a) @ X4) @ X4)))))).
% 3.06/1.67 thf(fact_228_process__term_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),X4:((proces554692349s_term @ A) @ B),Y:((proces554692349s_term @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: ((((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ X4) @ Y) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ X4)) => ((((member @ C) @ Y1) @ (((proces1264666542s_term @ C) @ D) @ Y)) => (((R1 @ Z1) @ Y1) => ((R1a @ Z1) @ Y1)))))) => ((! [Z2:B,Y23:D]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ X4)) => ((((member @ D) @ Y23) @ (((proces1493547885s_term @ C) @ D) @ Y)) => (((R22 @ Z2) @ Y23) => ((R2a @ Z2) @ Y23)))))) => ((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ X4) @ Y))))))).
% 3.06/1.67 thf(fact_229_process__term_Orel__cong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X4:((proces554692349s_term @ A) @ B),Ya:((proces554692349s_term @ A) @ B),Y:((proces554692349s_term @ C) @ D),Xa:((proces554692349s_term @ C) @ D),R1:(A > (C > $o)),R1a:(A > (C > $o)),R22:(B > (D > $o)),R2a:(B > (D > $o))]: (((X4 = Ya) => ((Y = Xa) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ Ya)) => ((((member @ C) @ Y1) @ (((proces1264666542s_term @ C) @ D) @ Xa)) => (((R1 @ Z1) @ Y1) = ((R1a @ Z1) @ Y1)))))) => ((! [Z2:B,Y23:D]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ Ya)) => ((((member @ D) @ Y23) @ (((proces1493547885s_term @ C) @ D) @ Xa)) => (((R22 @ Z2) @ Y23) = ((R2a @ Z2) @ Y23)))))) => (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ X4) @ Y) = ((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ Ya) @ Xa))))))))).
% 3.06/1.67 thf(fact_230_process__term_Omap__cong, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),Ya:((proces554692349s_term @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((X4 = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ Ya)) => ((F1 @ Z1) = (G1 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ Ya)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1) @ F2) @ X4) = (((((((proces224683037s_term @ A) @ C) @ B) @ D) @ G1) @ G2) @ Ya)))))))).
% 3.06/1.67 thf(fact_231_process__term_Omap__cong0, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ X4)) => ((F1 @ Z1) = (G1 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ X4)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1) @ F2) @ X4) = (((((((proces224683037s_term @ A) @ C) @ B) @ D) @ G1) @ G2) @ X4))))))).
% 3.06/1.67 thf(fact_232_process__term_Oinj__map__strong, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),Xa:((proces554692349s_term @ A) @ B),F1:(A > C),F1a:(A > C),F2:(B > D),F2a:(B > D)]: (((! [Z1:A,Z1a:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ X4)) => ((((member @ A) @ Z1a) @ (((proces1264666542s_term @ A) @ B) @ Xa)) => (((F1 @ Z1) = (F1a @ Z1a)) => (Z1 = Z1a)))))) => ((! [Z2:B,Z2a:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ X4)) => ((((member @ B) @ Z2a) @ (((proces1493547885s_term @ A) @ B) @ Xa)) => (((F2 @ Z2) = (F2a @ Z2a)) => (Z2 = Z2a)))))) => (((((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1) @ F2) @ X4) = (((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1a) @ F2a) @ Xa)) => (X4 = Xa))))))).
% 3.06/1.67 thf(fact_233_process__term_Osimps_I49_J, axiom, (! [A:$tType,Pvar:$tType,X14:Pvar]: (((((proces1493547885s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) = (((insert @ Pvar) @ X14) @ (bot_bot @ (set @ Pvar))))))).
% 3.06/1.67 thf(fact_234_process__term_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P22:(B > $o),X4:((proces554692349s_term @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: (((((((proces2118920028s_term @ A) @ B) @ P1) @ P22) @ X4) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ X4)) => ((P1 @ Z1) => (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ X4)) => ((P22 @ Z2) => (P2a @ Z2))))) => (((((proces2118920028s_term @ A) @ B) @ P1a) @ P2a) @ X4))))))).
% 3.06/1.67 thf(fact_235_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.06/1.67 thf(fact_236_singleton__conv, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ (^ [X:A]: ((X = A2)))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.06/1.67 thf(fact_237_singleton__conv2, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ A2)) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.06/1.67 thf(fact_238_process__term_Opred__inject_I1_J, axiom, (! [A:$tType,Pvar:$tType,P1:(A > $o),P22:(Pvar > $o),A2:Pvar]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A2)) = (P22 @ A2))))).
% 3.06/1.67 thf(fact_239_process__term_Opred__inject_I4_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P22:(Pvar > $o),A2:((proces554692349s_term @ A) @ Pvar),Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A2) @ Aa2)) = ((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ Aa2)))))).
% 3.06/1.67 thf(fact_240_process__term_Opred__inject_I3_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P22:(Pvar > $o),A2:A,Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A2) @ Aa2)) = ((P1 @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ Aa2)))))).
% 3.06/1.67 thf(fact_241_process__term_Osimps_I50_J, axiom, (! [A:$tType,Pvar:$tType,X2:(proces634752977rocess @ A)]: (((((proces1493547885s_term @ A) @ Pvar) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (bot_bot @ (set @ Pvar)))))).
% 3.06/1.67 thf(fact_242_process__term_Omap__cong__pred, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),Ya:((proces554692349s_term @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((X4 = Ya) => ((((((proces2118920028s_term @ A) @ B) @ (^ [Z12:A]: (((F1 @ Z12) = (G1 @ Z12))))) @ (^ [Z22:B]: (((F2 @ Z22) = (G2 @ Z22))))) @ Ya) => ((((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1) @ F2) @ X4) = (((((((proces224683037s_term @ A) @ C) @ B) @ D) @ G1) @ G2) @ Ya))))))).
% 3.06/1.67 thf(fact_243_process__term_Osimps_I45_J, axiom, (! [Pvar:$tType,A:$tType,X14:Pvar]: (((((proces1264666542s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X14)) = (bot_bot @ (set @ A)))))).
% 3.06/1.67 thf(fact_244_Collect__conv__if, axiom, (! [A:$tType,P6:(A > $o),A2:A]: ((((P6 @ A2) => (((collect @ A) @ (^ [X:A]: (((X = A2) & (P6 @ X))))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P6 @ A2))) => (((collect @ A) @ (^ [X:A]: (((X = A2) & (P6 @ X))))) = (bot_bot @ (set @ A)))))))).
% 3.06/1.67 thf(fact_245_Collect__conv__if2, axiom, (! [A:$tType,P6:(A > $o),A2:A]: ((((P6 @ A2) => (((collect @ A) @ (^ [X:A]: (((A2 = X) & (P6 @ X))))) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P6 @ A2))) => (((collect @ A) @ (^ [X:A]: (((A2 = X) & (P6 @ X))))) = (bot_bot @ (set @ A)))))))).
% 3.06/1.67 thf(fact_246_process__term_Opred__True, axiom, (! [B:$tType,A:$tType]: ((((((proces2118920028s_term @ A) @ B) @ (^ [Uu:A]: ($true))) @ (^ [Uu:B]: ($true))) = (^ [Uu:((proces554692349s_term @ A) @ B)]: ($true)))))).
% 3.06/1.67 thf(fact_247_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X:A]: ($false))))))).
% 3.06/1.67 thf(fact_248_singleton__inject, axiom, (! [A:$tType,A2:A,B3:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A2 = B3))))).
% 3.06/1.67 thf(fact_249_insert__not__empty, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((insert @ A) @ A2) @ A6) != (bot_bot @ (set @ A)))))).
% 3.06/1.67 thf(fact_250_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B3:A,C3:A,D2:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C3) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A2 = C3) & (B3 = D2)) | ((A2 = D2) & (B3 = C3))))))).
% 3.06/1.67 thf(fact_251_singleton__iff, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B3 = A2))))).
% 3.06/1.67 thf(fact_252_singletonD, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B3 = A2))))).
% 3.06/1.67 thf(fact_253_process__term_Opred__cong, axiom, (! [B:$tType,A:$tType,X4:((proces554692349s_term @ A) @ B),Ya:((proces554692349s_term @ A) @ B),P1:(A > $o),P1a:(A > $o),P22:(B > $o),P2a:(B > $o)]: (((X4 = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((proces1264666542s_term @ A) @ B) @ Ya)) => ((P1 @ Z1) = (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((proces1493547885s_term @ A) @ B) @ Ya)) => ((P22 @ Z2) = (P2a @ Z2))))) => ((((((proces2118920028s_term @ A) @ B) @ P1) @ P22) @ X4) = (((((proces2118920028s_term @ A) @ B) @ P1a) @ P2a) @ Ya)))))))).
% 3.06/1.67 thf(fact_254_the__elem__eq, axiom, (! [A:$tType,X4:A]: ((((the_elem @ A) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))) = X4)))).
% 3.06/1.67 thf(help_If_3_1_T, axiom, (! [P6:$o]: (((P6 = $true) | (P6 = $false))))).
% 3.06/1.67 thf(help_If_2_1_T, axiom, (! [A:$tType,X4:A,Y:A]: ((((((if @ A) @ $false) @ X4) @ Y) = Y)))).
% 3.06/1.67 thf(help_If_1_1_T, axiom, (! [A:$tType,X4:A,Y:A]: ((((((if @ A) @ $true) @ X4) @ Y) = X4)))).
% 3.06/1.67 thf(conj_0, conjecture, ((((proces10484146Action @ a) @ pa) = ((proces10484146Action @ a) @ p2)) & (((proces401113213Choice @ a) @ pa) = ((proces401113213Choice @ a) @ p2)))).
% 3.06/1.67 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2DTF1352.p
% 3.06/1.67 ------------------------
% 3.24/1.71 ---- Cleaned THF ---
% 3.24/1.71 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 3.24/1.71 proces554692349s_term: $tType > $tType > $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 3.24/1.71 proces634752977rocess: $tType > $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_t_Product__Type_Oprod,type,
% 3.24/1.71 product_prod: $tType > $tType > $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_t_Set_Oset,type,
% 3.24/1.71 set: $tType > $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_t_itself,type,
% 3.24/1.71 itself: $tType > $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_tf_b,type,
% 3.24/1.71 b: $tType ).
% 3.24/1.71
% 3.24/1.71 thf(ty_tf_a,type,
% 3.24/1.71 a: $tType ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_HOL_Oundefined,type,
% 3.24/1.71 undefined:
% 3.24/1.71 !>[A: $tType] : A ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_If,type,
% 3.24/1.71 if:
% 3.24/1.71 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.24/1.71 bot_bot:
% 3.24/1.71 !>[A: $tType] : A ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 3.24/1.71 proces1239275103le_CH1:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 3.24/1.71 proces1869379930H1_rel:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 3.24/1.71 proces1239275104le_CH2:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 3.24/1.71 proces93903513H2_rel:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 3.24/1.71 proces126235999e_CONT:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 3.24/1.71 proces1004198490NT_rel:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 3.24/1.71 proces1708129104e_PREF:
% 3.24/1.71 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 3.24/1.71 proces527360425EF_rel:
% 3.24/1.71 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 3.24/1.71 proces1121166967uarded:
% 3.24/1.71 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 3.24/1.71 proces687458811_isACT:
% 3.24/1.71 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 3.24/1.71 proces896239806CT_rel:
% 3.24/1.71 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 3.24/1.71 proces1525233512Action:
% 3.24/1.71 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 3.24/1.71 proces1915862579Choice:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 3.24/1.71 proces1406508781rocess:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 3.24/1.71 proces979765041_ch1Of:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 3.24/1.71 proces988026546_ch2Of:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 3.24/1.71 proces1778668539contOf:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 3.24/1.71 proces894737309rocess:
% 3.24/1.71 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 3.24/1.71 proces10484146Action:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 3.24/1.71 proces401113213Choice:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 3.24/1.71 proces370407749rocess:
% 3.24/1.71 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 3.24/1.71 proces745025900prefOf:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 3.24/1.71 proces749077512rocess:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process,type,
% 3.24/1.71 proces1148692671rocess:
% 3.24/1.71 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( set @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 3.24/1.71 proces1454156180ss_ACT:
% 3.24/1.71 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 3.24/1.71 proces89589571ess_CH:
% 3.24/1.71 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 3.24/1.71 proces1062592052s_PROC:
% 3.24/1.71 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 3.24/1.71 proces1627516585ss_VAR:
% 3.24/1.71 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 3.24/1.71 proces460752237s_term:
% 3.24/1.71 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 3.24/1.71 proces224683037s_term:
% 3.24/1.71 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 3.24/1.71 proces2118920028s_term:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 3.24/1.71 proces2029722208s_term:
% 3.24/1.71 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset1__process__term,type,
% 3.24/1.71 proces1264666542s_term:
% 3.24/1.71 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 3.24/1.71 proces1493547885s_term:
% 3.24/1.71 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 3.24/1.71 proces1652378886lution:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Product__Type_OPair,type,
% 3.24/1.71 product_Pair:
% 3.24/1.71 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Pure_Otype,type,
% 3.24/1.71 type:
% 3.24/1.71 !>[A: $tType] : ( itself @ A ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Set_OCollect,type,
% 3.24/1.71 collect:
% 3.24/1.71 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Set_Oinsert,type,
% 3.24/1.71 insert:
% 3.24/1.71 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Set_Othe__elem,type,
% 3.24/1.71 the_elem:
% 3.24/1.71 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_Wellfounded_Oaccp,type,
% 3.24/1.71 accp:
% 3.24/1.71 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_c_member,type,
% 3.24/1.71 member:
% 3.24/1.71 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.24/1.71
% 3.24/1.71 thf(sy_v_p,type,
% 3.24/1.71 p: proces634752977rocess @ a ).
% 3.24/1.71
% 3.24/1.71 thf(sy_v_p_H____,type,
% 3.24/1.71 p2: proces634752977rocess @ a ).
% 3.24/1.71
% 3.24/1.71 thf(sy_v_pa____,type,
% 3.24/1.71 pa: proces634752977rocess @ a ).
% 3.24/1.71
% 3.24/1.71 thf(sy_v_q____,type,
% 3.24/1.71 q: proces634752977rocess @ a ).
% 3.24/1.71
% 3.24/1.71 thf(sy_v_sys,type,
% 3.24/1.71 sys: b > ( proces554692349s_term @ a @ b ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062,axiom,
% 3.24/1.71 ( ( proces10484146Action @ a @ pa )
% 3.24/1.71 | ( proces401113213Choice @ a @ pa ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_1_process_Odistinct__disc_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces401113213Choice @ A @ Process )
% 3.24/1.71 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_2_process_Odistinct__disc_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces10484146Action @ A @ Process )
% 3.24/1.71 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_3_isAction__isChoice,axiom,
% 3.24/1.71 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces10484146Action @ A @ P )
% 3.24/1.71 | ( proces401113213Choice @ A @ P ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_4_process_Oexhaust__disc,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.71 ( ~ ( proces10484146Action @ A @ Process )
% 3.24/1.71 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_5_not__isAction__isChoice,axiom,
% 3.24/1.71 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.24/1.71 ~ ( ( proces10484146Action @ A @ P )
% 3.24/1.71 & ( proces401113213Choice @ A @ P ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_6_process_Ocorec__disc__iff_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 3.24/1.71 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.71 = ( ~ ( P @ A2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_7_process_Ocorec__disc__iff_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 3.24/1.71 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.71 = ( P @ A2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_8_iss,axiom,
% 3.24/1.71 ( p2
% 3.24/1.71 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_9_process_Omap__disc__iff_I2_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( proces401113213Choice @ A @ A2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_10_process_Ocorec__disc_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.71 ( ~ ( P @ A2 )
% 3.24/1.71 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_11_process_Omap__disc__iff_I1_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( proces10484146Action @ A @ A2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_12_process_Ocorec__disc_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.71 ( ( P @ A2 )
% 3.24/1.71 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_13_process_Odisc_I4_J,axiom,
% 3.24/1.71 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_14_process_Odisc_I3_J,axiom,
% 3.24/1.71 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.71 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_15_process_OdiscI_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Process
% 3.24/1.71 = ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 3.24/1.71 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_16_isChoice__def,axiom,
% 3.24/1.71 ! [A: $tType] :
% 3.24/1.71 ( ( proces401113213Choice @ A )
% 3.24/1.71 = ( ^ [Process2: proces634752977rocess @ A] :
% 3.24/1.71 ? [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.24/1.71 ( Process2
% 3.24/1.71 = ( proces1915862579Choice @ A @ X212 @ X222 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_17_process_Odisc_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.71 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_18_process__term_Oinject_I2_J,axiom,
% 3.24/1.71 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 3.24/1.71 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.24/1.71 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 3.24/1.71 = ( X2 = Y2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_19_process_Oinject_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 3.24/1.71 ( ( ( proces1525233512Action @ A @ X11 @ X12 )
% 3.24/1.71 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 3.24/1.71 = ( ( X11 = Y11 )
% 3.24/1.71 & ( X12 = Y12 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_20_process_Oinject_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 3.24/1.71 ( ( ( proces1915862579Choice @ A @ X21 @ X22 )
% 3.24/1.71 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 3.24/1.71 = ( ( X21 = Y21 )
% 3.24/1.71 & ( X22 = Y22 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 3.24/1.71 ( q
% 3.24/1.71 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_22_process_Ocorec_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.71 ( ~ ( P @ A2 )
% 3.24/1.71 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 3.24/1.71 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_23_process_Ocorec_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.71 ( ( P @ A2 )
% 3.24/1.71 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 3.24/1.71 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_24_process_Osimps_I16_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 3.24/1.71 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X22 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_25_process_Osimps_I15_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,F: A > B,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.71 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X12 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_26_process_Odistinct_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces1525233512Action @ A @ X11 @ X12 )
% 3.24/1.71 != ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_27_process_Oexhaust,axiom,
% 3.24/1.71 ! [A: $tType,Y: proces634752977rocess @ A] :
% 3.24/1.71 ( ! [X112: A,X122: proces634752977rocess @ A] :
% 3.24/1.71 ( Y
% 3.24/1.71 != ( proces1525233512Action @ A @ X112 @ X122 ) )
% 3.24/1.71 => ~ ! [X213: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.24/1.71 ( Y
% 3.24/1.71 != ( proces1915862579Choice @ A @ X213 @ X223 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_28_process_Ocorec__code,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType] :
% 3.24/1.71 ( ( proces894737309rocess @ C @ A )
% 3.24/1.71 = ( ^ [P2: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A3: C] : ( if @ ( proces634752977rocess @ A ) @ ( P2 @ A3 ) @ ( proces1525233512Action @ A @ ( G112 @ A3 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A3 ) @ ( G1212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A3 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A3 ) @ ( G2112 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A3 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A3 ) @ ( G2212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A3 ) ) ) ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_29_process_Omap__ident,axiom,
% 3.24/1.71 ! [A: $tType,T: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces370407749rocess @ A @ A
% 3.24/1.71 @ ^ [X: A] : X
% 3.24/1.71 @ T )
% 3.24/1.71 = T ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_30_process__strong__coind,axiom,
% 3.24/1.71 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ P @ P3 )
% 3.24/1.71 => ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ P4 @ P5 )
% 3.24/1.71 => ( ( ( proces10484146Action @ A @ P4 )
% 3.24/1.71 = ( proces10484146Action @ A @ P5 ) )
% 3.24/1.71 & ( ( proces401113213Choice @ A @ P4 )
% 3.24/1.71 = ( proces401113213Choice @ A @ P5 ) ) ) )
% 3.24/1.71 => ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
% 3.24/1.71 => ( ( A4 = A5 )
% 3.24/1.71 & ( ( Phi @ P4 @ P5 )
% 3.24/1.71 | ( P4 = P5 ) ) ) )
% 3.24/1.71 => ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
% 3.24/1.71 => ( ( ( Phi @ P4 @ P5 )
% 3.24/1.71 | ( P4 = P5 ) )
% 3.24/1.71 & ( ( Phi @ Q @ Q2 )
% 3.24/1.71 | ( Q = Q2 ) ) ) )
% 3.24/1.71 => ( P = P3 ) ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_31_process__coind,axiom,
% 3.24/1.71 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ P @ P3 )
% 3.24/1.71 => ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ P4 @ P5 )
% 3.24/1.71 => ( ( ( proces10484146Action @ A @ P4 )
% 3.24/1.71 = ( proces10484146Action @ A @ P5 ) )
% 3.24/1.71 & ( ( proces401113213Choice @ A @ P4 )
% 3.24/1.71 = ( proces401113213Choice @ A @ P5 ) ) ) )
% 3.24/1.71 => ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
% 3.24/1.71 => ( ( A4 = A5 )
% 3.24/1.71 & ( Phi @ P4 @ P5 ) ) )
% 3.24/1.71 => ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
% 3.24/1.71 => ( ( Phi @ P4 @ P5 )
% 3.24/1.71 & ( Phi @ Q @ Q2 ) ) )
% 3.24/1.71 => ( P = P3 ) ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_32_isAction__def,axiom,
% 3.24/1.71 ! [A: $tType] :
% 3.24/1.71 ( ( proces10484146Action @ A )
% 3.24/1.71 = ( ^ [Process2: proces634752977rocess @ A] :
% 3.24/1.71 ? [X113: A,X123: proces634752977rocess @ A] :
% 3.24/1.71 ( Process2
% 3.24/1.71 = ( proces1525233512Action @ A @ X113 @ X123 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_33_process_OdiscI_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.71 ( ( Process
% 3.24/1.71 = ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.71 => ( proces10484146Action @ A @ Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_34_process_Odisc_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_35_solution_Odisc__iff_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.71 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.71 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_36_solution_Odisc__iff_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.71 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.71 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_37_solution_Odisc_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.71 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.71 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_38_solution_Odisc_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.71 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.71 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_39_process_Omap__sel_I1_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.24/1.71 ( ( proces10484146Action @ A @ A2 )
% 3.24/1.71 => ( ( proces745025900prefOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( F @ ( proces745025900prefOf @ A @ A2 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_40_process_Omap__sel_I3_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.24/1.71 ( ( proces401113213Choice @ A @ A2 )
% 3.24/1.71 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_41_process_Omap__sel_I4_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.24/1.71 ( ( proces401113213Choice @ A @ A2 )
% 3.24/1.71 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_42_isACT_Osimps_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 3.24/1.71 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 3.24/1.71 = ( proces10484146Action @ D @ P ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_43_process_Omap__sel_I2_J,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.24/1.71 ( ( proces10484146Action @ A @ A2 )
% 3.24/1.71 => ( ( proces1778668539contOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.24/1.71 = ( proces370407749rocess @ A @ B @ F @ ( proces1778668539contOf @ A @ A2 ) ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_44_process_Odisc__eq__case_I2_J,axiom,
% 3.24/1.71 ! [A: $tType] :
% 3.24/1.71 ( ( proces401113213Choice @ A )
% 3.24/1.71 = ( proces1406508781rocess @ A @ $o
% 3.24/1.71 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $false
% 3.24/1.71 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $true ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_45_mem__Collect__eq,axiom,
% 3.24/1.71 ! [A: $tType,A2: A,P6: A > $o] :
% 3.24/1.71 ( ( member @ A @ A2 @ ( collect @ A @ P6 ) )
% 3.24/1.71 = ( P6 @ A2 ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_46_Collect__mem__eq,axiom,
% 3.24/1.71 ! [A: $tType,A6: set @ A] :
% 3.24/1.71 ( ( collect @ A
% 3.24/1.71 @ ^ [X: A] : ( member @ A @ X @ A6 ) )
% 3.24/1.71 = A6 ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_47_Collect__cong,axiom,
% 3.24/1.71 ! [A: $tType,P6: A > $o,Q3: A > $o] :
% 3.24/1.71 ( ! [X3: A] :
% 3.24/1.71 ( ( P6 @ X3 )
% 3.24/1.71 = ( Q3 @ X3 ) )
% 3.24/1.71 => ( ( collect @ A @ P6 )
% 3.24/1.71 = ( collect @ A @ Q3 ) ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_48_ext,axiom,
% 3.24/1.71 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.24/1.71 ( ! [X3: A] :
% 3.24/1.71 ( ( F @ X3 )
% 3.24/1.71 = ( G @ X3 ) )
% 3.24/1.71 => ( F = G ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_49_process_Ocollapse_I1_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces10484146Action @ A @ Process )
% 3.24/1.71 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 3.24/1.71 = Process ) ) ).
% 3.24/1.71
% 3.24/1.71 thf(fact_50_process_Ocollapse_I2_J,axiom,
% 3.24/1.71 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.71 ( ( proces401113213Choice @ A @ Process )
% 3.24/1.71 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 3.24/1.72 = Process ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_51_process_Osplit__sel,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.24/1.72 ( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.24/1.72 = ( ( ( Process
% 3.24/1.72 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.24/1.72 => ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.24/1.72 & ( ( Process
% 3.24/1.72 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.24/1.72 => ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_52_process_Ocase__eq__if,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces1406508781rocess @ A @ B )
% 3.24/1.72 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_53_process_Osplit__sel__asm,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.24/1.72 ( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.24/1.72 = ( ~ ( ( ( Process
% 3.24/1.72 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.24/1.72 & ~ ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.24/1.72 | ( ( Process
% 3.24/1.72 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.24/1.72 & ~ ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_54_process_Oexhaust__sel,axiom,
% 3.24/1.72 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.24/1.72 ( ( Process
% 3.24/1.72 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.24/1.72 => ( Process
% 3.24/1.72 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_55_process_Oexpand,axiom,
% 3.24/1.72 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.24/1.72 ( ( ( proces10484146Action @ A @ Process )
% 3.24/1.72 = ( proces10484146Action @ A @ Process3 ) )
% 3.24/1.72 => ( ( ( proces10484146Action @ A @ Process )
% 3.24/1.72 => ( ( proces10484146Action @ A @ Process3 )
% 3.24/1.72 => ( ( ( proces745025900prefOf @ A @ Process )
% 3.24/1.72 = ( proces745025900prefOf @ A @ Process3 ) )
% 3.24/1.72 & ( ( proces1778668539contOf @ A @ Process )
% 3.24/1.72 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 3.24/1.72 => ( ( ( proces401113213Choice @ A @ Process )
% 3.24/1.72 => ( ( proces401113213Choice @ A @ Process3 )
% 3.24/1.72 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 3.24/1.72 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 3.24/1.72 & ( ( proces988026546_ch2Of @ A @ Process )
% 3.24/1.72 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 3.24/1.72 => ( Process = Process3 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_56_process_Ocoinduct,axiom,
% 3.24/1.72 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.24/1.72 ( ( R @ Process @ Process3 )
% 3.24/1.72 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 3.24/1.72 ( ( R @ Process4 @ Process5 )
% 3.24/1.72 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 = ( proces10484146Action @ A @ Process5 ) )
% 3.24/1.72 & ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 => ( ( proces10484146Action @ A @ Process5 )
% 3.24/1.72 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 3.24/1.72 = ( proces745025900prefOf @ A @ Process5 ) )
% 3.24/1.72 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 3.24/1.72 & ( ( proces401113213Choice @ A @ Process4 )
% 3.24/1.72 => ( ( proces401113213Choice @ A @ Process5 )
% 3.24/1.72 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 3.24/1.72 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 3.24/1.72 => ( Process = Process3 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_57_process_Ocoinduct__strong,axiom,
% 3.24/1.72 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.24/1.72 ( ( R @ Process @ Process3 )
% 3.24/1.72 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 3.24/1.72 ( ( R @ Process4 @ Process5 )
% 3.24/1.72 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 = ( proces10484146Action @ A @ Process5 ) )
% 3.24/1.72 & ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 => ( ( proces10484146Action @ A @ Process5 )
% 3.24/1.72 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 3.24/1.72 = ( proces745025900prefOf @ A @ Process5 ) )
% 3.24/1.72 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 3.24/1.72 | ( ( proces1778668539contOf @ A @ Process4 )
% 3.24/1.72 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 3.24/1.72 & ( ( proces401113213Choice @ A @ Process4 )
% 3.24/1.72 => ( ( proces401113213Choice @ A @ Process5 )
% 3.24/1.72 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 3.24/1.72 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 3.24/1.72 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 3.24/1.72 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 3.24/1.72 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 3.24/1.72 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 3.24/1.72 => ( Process = Process3 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_58_process_Ocase__distrib,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.24/1.72 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.24/1.72 = ( proces1406508781rocess @ A @ C
% 3.24/1.72 @ ^ [X1: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X1 @ X23 ) )
% 3.24/1.72 @ ^ [X1: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X1 @ X23 ) )
% 3.24/1.72 @ Process ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_59_process_Osel_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.72 = X12 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_60_process_Osel_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 3.24/1.72 = X21 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_61_process_Osel_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 3.24/1.72 = X22 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_62_process_Osel_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.72 = X11 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_63_process_Ocorec__sel_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.72 ( ( P @ A2 )
% 3.24/1.72 => ( ( ( Q12 @ A2 )
% 3.24/1.72 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( G121 @ A2 ) ) )
% 3.24/1.72 & ( ~ ( Q12 @ A2 )
% 3.24/1.72 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_64_process_Ocorec__sel_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.72 ( ~ ( P @ A2 )
% 3.24/1.72 => ( ( ( Q21 @ A2 )
% 3.24/1.72 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( G211 @ A2 ) ) )
% 3.24/1.72 & ( ~ ( Q21 @ A2 )
% 3.24/1.72 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_65_process_Ocorec__sel_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.72 ( ~ ( P @ A2 )
% 3.24/1.72 => ( ( ( Q22 @ A2 )
% 3.24/1.72 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( G221 @ A2 ) ) )
% 3.24/1.72 & ( ~ ( Q22 @ A2 )
% 3.24/1.72 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_66_process_Ocorec__sel_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.24/1.72 ( ( P @ A2 )
% 3.24/1.72 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.24/1.72 = ( G11 @ A2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_67_process_Osimps_I5_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.72 = ( F1 @ X11 @ X12 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_68_process_Osimps_I6_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 3.24/1.72 = ( F2 @ X21 @ X22 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_69_process_Odisc__eq__case_I1_J,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces10484146Action @ A )
% 3.24/1.72 = ( proces1406508781rocess @ A @ $o
% 3.24/1.72 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $true
% 3.24/1.72 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $false ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_70_solution_Osimps_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.72 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_71_solution_Osimps_I5_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.72 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_72_solution_Osimps_I6_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.72 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_73_solution_Osimps_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.24/1.72 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_74_process_Orel__coinduct,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,P6: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 3.24/1.72 ( ( P6 @ X4 @ Y )
% 3.24/1.72 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 3.24/1.72 ( ( P6 @ Process4 @ Process5 )
% 3.24/1.72 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 = ( proces10484146Action @ B @ Process5 ) )
% 3.24/1.72 & ( ( proces10484146Action @ A @ Process4 )
% 3.24/1.72 => ( ( proces10484146Action @ B @ Process5 )
% 3.24/1.72 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 3.24/1.72 & ( P6 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 3.24/1.72 & ( ( proces401113213Choice @ A @ Process4 )
% 3.24/1.72 => ( ( proces401113213Choice @ B @ Process5 )
% 3.24/1.72 => ( ( P6 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 3.24/1.72 & ( P6 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 3.24/1.72 => ( proces749077512rocess @ A @ B @ R @ X4 @ Y ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_75_process_Orel__sel,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B )
% 3.24/1.72 = ( ^ [R2: A > B > $o,A3: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 3.24/1.72 ( ( ( proces10484146Action @ A @ A3 )
% 3.24/1.72 = ( proces10484146Action @ B @ B2 ) )
% 3.24/1.72 & ( ( proces10484146Action @ A @ A3 )
% 3.24/1.72 => ( ( proces10484146Action @ B @ B2 )
% 3.24/1.72 => ( ( R2 @ ( proces745025900prefOf @ A @ A3 ) @ ( proces745025900prefOf @ B @ B2 ) )
% 3.24/1.72 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A3 ) @ ( proces1778668539contOf @ B @ B2 ) ) ) ) )
% 3.24/1.72 & ( ( proces401113213Choice @ A @ A3 )
% 3.24/1.72 => ( ( proces401113213Choice @ B @ B2 )
% 3.24/1.72 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A3 ) @ ( proces979765041_ch1Of @ B @ B2 ) )
% 3.24/1.72 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A3 ) @ ( proces988026546_ch2Of @ B @ B2 ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_76_PREF_Osimps_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.24/1.72 = ( proces745025900prefOf @ B @ P ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_77_CH2_Osimps_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_78_process_Orel__inject_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 3.24/1.72 = ( ( R @ X11 @ Y11 )
% 3.24/1.72 & ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_79_process_Orel__inject_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 3.24/1.72 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 3.24/1.72 & ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_80_process_Orel__eq,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ A
% 3.24/1.72 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.24/1.72 = ( ^ [Y3: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y3 = Z ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_81_process_Orel__refl,axiom,
% 3.24/1.72 ! [B: $tType,Ra: B > B > $o,X4: proces634752977rocess @ B] :
% 3.24/1.72 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 3.24/1.72 => ( proces749077512rocess @ B @ B @ Ra @ X4 @ X4 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_82_process_Orel__intros_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X12: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 3.24/1.72 ( ( R @ X11 @ Y11 )
% 3.24/1.72 => ( ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 )
% 3.24/1.72 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_83_process_Orel__intros_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X22: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 3.24/1.72 => ( ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 )
% 3.24/1.72 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_84_process_Orel__map_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,B: $tType,Sa: A > C > $o,X4: proces634752977rocess @ A,G: B > C,Y: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ C @ Sa @ X4 @ ( proces370407749rocess @ B @ C @ G @ Y ) )
% 3.24/1.72 = ( proces749077512rocess @ A @ B
% 3.24/1.72 @ ^ [X: A,Y4: B] : ( Sa @ X @ ( G @ Y4 ) )
% 3.24/1.72 @ X4
% 3.24/1.72 @ Y ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_85_process_Orel__map_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,B: $tType,Sb: C > B > $o,I: A > C,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ C @ B @ Sb @ ( proces370407749rocess @ A @ C @ I @ X4 ) @ Y )
% 3.24/1.72 = ( proces749077512rocess @ A @ B
% 3.24/1.72 @ ^ [X: A] : ( Sb @ ( I @ X ) )
% 3.24/1.72 @ X4
% 3.24/1.72 @ Y ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_86_solution_Ocode,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces1652378886lution @ A @ B )
% 3.24/1.72 = ( ^ [Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys2 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces126235999e_CONT @ A @ B @ Sys2 @ T3 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275103le_CH1 @ A @ B @ Sys2 @ T3 ) ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275104le_CH2 @ A @ B @ Sys2 @ T3 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_87_process_Orel__distinct_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X12: proces634752977rocess @ B] :
% 3.24/1.72 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X12 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_88_process_Orel__distinct_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.24/1.72 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_89_process_Orel__cases,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B3: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B3 )
% 3.24/1.72 => ( ! [X13: A,X24: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1525233512Action @ A @ X13 @ X24 ) )
% 3.24/1.72 => ! [Y1: B,Y23: proces634752977rocess @ B] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces1525233512Action @ B @ Y1 @ Y23 ) )
% 3.24/1.72 => ( ( R @ X13 @ Y1 )
% 3.24/1.72 => ~ ( proces749077512rocess @ A @ B @ R @ X24 @ Y23 ) ) ) )
% 3.24/1.72 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 3.24/1.72 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 3.24/1.72 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 3.24/1.72 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_90_solution_Octr_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.24/1.72 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_91_solution_Octr_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.24/1.72 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.24/1.72 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_92_CONT_Osimps_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_93_CH1_Osimps_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_94_prefOf__def,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces745025900prefOf @ A )
% 3.24/1.72 = ( proces1406508781rocess @ A @ A
% 3.24/1.72 @ ^ [X113: A,X123: proces634752977rocess @ A] : X113
% 3.24/1.72 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_95_process_Oset__sel_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,A2: proces634752977rocess @ A,Xa: A] :
% 3.24/1.72 ( ( proces401113213Choice @ A @ A2 )
% 3.24/1.72 => ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces979765041_ch1Of @ A @ A2 ) ) )
% 3.24/1.72 => ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_96_process_Oset__sel_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,A2: proces634752977rocess @ A,Xb: A] :
% 3.24/1.72 ( ( proces401113213Choice @ A @ A2 )
% 3.24/1.72 => ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces988026546_ch2Of @ A @ A2 ) ) )
% 3.24/1.72 => ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_97_process_Oset__sel_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,A2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces10484146Action @ A @ A2 )
% 3.24/1.72 => ( member @ A @ ( proces745025900prefOf @ A @ A2 ) @ ( proces1148692671rocess @ A @ A2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_98_process_Oset__sel_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,A2: proces634752977rocess @ A,X4: A] :
% 3.24/1.72 ( ( proces10484146Action @ A @ A2 )
% 3.24/1.72 => ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
% 3.24/1.72 => ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_99_process_Oset__cases,axiom,
% 3.24/1.72 ! [A: $tType,E: A,A2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( member @ A @ E @ ( proces1148692671rocess @ A @ A2 ) )
% 3.24/1.72 => ( ! [Z2: proces634752977rocess @ A] :
% 3.24/1.72 ( A2
% 3.24/1.72 != ( proces1525233512Action @ A @ E @ Z2 ) )
% 3.24/1.72 => ( ! [Z1: A,Z2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) )
% 3.24/1.72 => ( ! [Z1: proces634752977rocess @ A] :
% 3.24/1.72 ( ? [Z2: proces634752977rocess @ A] :
% 3.24/1.72 ( A2
% 3.24/1.72 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z1 ) ) )
% 3.24/1.72 => ~ ! [Z1: proces634752977rocess @ A,Z2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_100_process_Orel__refl__strong,axiom,
% 3.24/1.72 ! [A: $tType,X4: proces634752977rocess @ A,Ra: A > A > $o] :
% 3.24/1.72 ( ! [Z3: A] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 3.24/1.72 => ( Ra @ Z3 @ Z3 ) )
% 3.24/1.72 => ( proces749077512rocess @ A @ A @ Ra @ X4 @ X4 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_101_process_Orel__mono__strong,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,R: A > B > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,Ra: A > B > $o] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
% 3.24/1.72 => ( ! [Z3: A,Yb: B] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 3.24/1.72 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y ) )
% 3.24/1.72 => ( ( R @ Z3 @ Yb )
% 3.24/1.72 => ( Ra @ Z3 @ Yb ) ) ) )
% 3.24/1.72 => ( proces749077512rocess @ A @ B @ Ra @ X4 @ Y ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_102_process_Orel__cong,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,Y: proces634752977rocess @ B,Xa: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ( Y = Xa )
% 3.24/1.72 => ( ! [Z3: A,Yb: B] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
% 3.24/1.72 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa ) )
% 3.24/1.72 => ( ( R @ Z3 @ Yb )
% 3.24/1.72 = ( Ra @ Z3 @ Yb ) ) ) )
% 3.24/1.72 => ( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
% 3.24/1.72 = ( proces749077512rocess @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_103_process_Oset__intros_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,A1: A,A22: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_104_process_Oset__intros_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,A22: proces634752977rocess @ A,A1: A] :
% 3.24/1.72 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A22 ) )
% 3.24/1.72 => ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_105_process_Oset__intros_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,Xa: A,A1a: proces634752977rocess @ A,A2a: proces634752977rocess @ A] :
% 3.24/1.72 ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A1a ) )
% 3.24/1.72 => ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_106_process_Oset__intros_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,Xb: A,A2a: proces634752977rocess @ A,A1a: proces634752977rocess @ A] :
% 3.24/1.72 ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2a ) )
% 3.24/1.72 => ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_107_process_Oinj__map__strong,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Xa: proces634752977rocess @ A,F: A > B,Fa: A > B] :
% 3.24/1.72 ( ! [Z3: A,Za: A] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 3.24/1.72 => ( ( member @ A @ Za @ ( proces1148692671rocess @ A @ Xa ) )
% 3.24/1.72 => ( ( ( F @ Z3 )
% 3.24/1.72 = ( Fa @ Za ) )
% 3.24/1.72 => ( Z3 = Za ) ) ) )
% 3.24/1.72 => ( ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 3.24/1.72 = ( proces370407749rocess @ A @ B @ Fa @ Xa ) )
% 3.24/1.72 => ( X4 = Xa ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_108_process_Omap__cong0,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,F: A > B,G: A > B] :
% 3.24/1.72 ( ! [Z3: A] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
% 3.24/1.72 => ( ( F @ Z3 )
% 3.24/1.72 = ( G @ Z3 ) ) )
% 3.24/1.72 => ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 3.24/1.72 = ( proces370407749rocess @ A @ B @ G @ X4 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_109_process_Omap__cong,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,F: A > B,G: A > B] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ! [Z3: A] :
% 3.24/1.72 ( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
% 3.24/1.72 => ( ( F @ Z3 )
% 3.24/1.72 = ( G @ Z3 ) ) )
% 3.24/1.72 => ( ( proces370407749rocess @ A @ B @ F @ X4 )
% 3.24/1.72 = ( proces370407749rocess @ A @ B @ G @ Ya ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_110_contOf__def,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces1778668539contOf @ A )
% 3.24/1.72 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.24/1.72 @ ^ [X113: A,X123: proces634752977rocess @ A] : X123
% 3.24/1.72 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_111_ch1Of__def,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces979765041_ch1Of @ A )
% 3.24/1.72 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.24/1.72 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.24/1.72 @ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X212 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_112_ch2Of__def,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( proces988026546_ch2Of @ A )
% 3.24/1.72 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.24/1.72 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.24/1.72 @ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_113_process_Oset__induct,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,A2: proces634752977rocess @ A,P6: A > ( proces634752977rocess @ A ) > $o] :
% 3.24/1.72 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) )
% 3.24/1.72 => ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P6 @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 3.24/1.72 => ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa2: A] :
% 3.24/1.72 ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ Z2 ) )
% 3.24/1.72 => ( ( P6 @ Xa2 @ Z2 )
% 3.24/1.72 => ( P6 @ Xa2 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
% 3.24/1.72 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb2: A] :
% 3.24/1.72 ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ Z1a ) )
% 3.24/1.72 => ( ( P6 @ Xb2 @ Z1a )
% 3.24/1.72 => ( P6 @ Xb2 @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 3.24/1.72 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc: A] :
% 3.24/1.72 ( ( member @ A @ Xc @ ( proces1148692671rocess @ A @ Z2a ) )
% 3.24/1.72 => ( ( P6 @ Xc @ Z2a )
% 3.24/1.72 => ( P6 @ Xc @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 3.24/1.72 => ( P6 @ X4 @ A2 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_114_process_Osimps_I21_J,axiom,
% 3.24/1.72 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 3.24/1.72 = ( insert @ A @ X11 @ ( proces1148692671rocess @ A @ X12 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_115_process__term_Osimps_I46_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.24/1.72 = ( proces1148692671rocess @ A @ X2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_116_process__term_Oset__intros_I1_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X4: A,Aa2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ Aa2 ) )
% 3.24/1.72 => ( member @ A @ X4 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ Aa2 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_117_process__term_Osimps_I26_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,C: $tType,B: $tType,A: $tType,F1: A > B,F2: Pvar > C,X2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ C @ ( proces370407749rocess @ A @ B @ F1 @ X2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_118_PREF_Osimps_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
% 3.24/1.72 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 3.24/1.72 = ( proces460752237s_term @ C @ B @ B
% 3.24/1.72 @ ^ [Aa3: C] : ( undefined @ B )
% 3.24/1.72 @ ( proces745025900prefOf @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.24/1.72 @ ( Sys @ X5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_119_process__term_Oinject_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,X14: Pvar,Y13: Pvar] :
% 3.24/1.72 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 3.24/1.72 = ( proces1627516585ss_VAR @ Pvar @ A @ Y13 ) )
% 3.24/1.72 = ( X14 = Y13 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_120_process__term_Ocase__distrib,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 3.24/1.72 = ( proces460752237s_term @ Pvar @ C @ A
% 3.24/1.72 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 3.24/1.72 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 3.24/1.72 @ ^ [X1: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X1 @ X23 ) )
% 3.24/1.72 @ ^ [X1: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X1 @ X23 ) )
% 3.24/1.72 @ Process_term ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_121_process__term_Omap__ident,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,T: proces554692349s_term @ A @ B] :
% 3.24/1.72 ( ( proces224683037s_term @ A @ A @ B @ B
% 3.24/1.72 @ ^ [X: A] : X
% 3.24/1.72 @ ^ [X: B] : X
% 3.24/1.72 @ T )
% 3.24/1.72 = T ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_122_process__term_Osimps_I25_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X14: Pvar] :
% 3.24/1.72 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 3.24/1.72 = ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X14 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_123_process__term_Osimps_I17_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X14: Pvar] :
% 3.24/1.72 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 3.24/1.72 = ( F1 @ X14 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_124_process__term_Odistinct_I1_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X14: Pvar,X2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 3.24/1.72 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_125_isACT_Osimps_I1_J,axiom,
% 3.24/1.72 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X5 ) )
% 3.24/1.72 = ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( Sys @ X5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_126_process__term_Osimps_I18_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.24/1.72 = ( F2 @ X2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_127_CONT_Osimps_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 3.24/1.72 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ( Sys @ X5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_128_CH2_Osimps_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 3.24/1.72 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 3.24/1.72 @ ( Sys @ X5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_129_CH1_Osimps_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 3.24/1.72 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 3.24/1.72 @ ( Sys @ X5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_130_insertCI,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 3.24/1.72 ( ( ~ ( member @ A @ A2 @ B4 )
% 3.24/1.72 => ( A2 = B3 ) )
% 3.24/1.72 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_131_insert__iff,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B3: A,A6: set @ A] :
% 3.24/1.72 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
% 3.24/1.72 = ( ( A2 = B3 )
% 3.24/1.72 | ( member @ A @ A2 @ A6 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_132_insert__absorb2,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,A6: set @ A] :
% 3.24/1.72 ( ( insert @ A @ X4 @ ( insert @ A @ X4 @ A6 ) )
% 3.24/1.72 = ( insert @ A @ X4 @ A6 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_133_solution__VAR,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 3.24/1.72 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.24/1.72 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
% 3.24/1.72 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_134_mk__disjoint__insert,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,A6: set @ A] :
% 3.24/1.72 ( ( member @ A @ A2 @ A6 )
% 3.24/1.72 => ? [B5: set @ A] :
% 3.24/1.72 ( ( A6
% 3.24/1.72 = ( insert @ A @ A2 @ B5 ) )
% 3.24/1.72 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_135_insert__commute,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,Y: A,A6: set @ A] :
% 3.24/1.72 ( ( insert @ A @ X4 @ ( insert @ A @ Y @ A6 ) )
% 3.24/1.72 = ( insert @ A @ Y @ ( insert @ A @ X4 @ A6 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_136_insert__eq__iff,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,A6: set @ A,B3: A,B4: set @ A] :
% 3.24/1.72 ( ~ ( member @ A @ A2 @ A6 )
% 3.24/1.72 => ( ~ ( member @ A @ B3 @ B4 )
% 3.24/1.72 => ( ( ( insert @ A @ A2 @ A6 )
% 3.24/1.72 = ( insert @ A @ B3 @ B4 ) )
% 3.24/1.72 = ( ( ( A2 = B3 )
% 3.24/1.72 => ( A6 = B4 ) )
% 3.24/1.72 & ( ( A2 != B3 )
% 3.24/1.72 => ? [C2: set @ A] :
% 3.24/1.72 ( ( A6
% 3.24/1.72 = ( insert @ A @ B3 @ C2 ) )
% 3.24/1.72 & ~ ( member @ A @ B3 @ C2 )
% 3.24/1.72 & ( B4
% 3.24/1.72 = ( insert @ A @ A2 @ C2 ) )
% 3.24/1.72 & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_137_insert__absorb,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,A6: set @ A] :
% 3.24/1.72 ( ( member @ A @ A2 @ A6 )
% 3.24/1.72 => ( ( insert @ A @ A2 @ A6 )
% 3.24/1.72 = A6 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_138_insert__ident,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,A6: set @ A,B4: set @ A] :
% 3.24/1.72 ( ~ ( member @ A @ X4 @ A6 )
% 3.24/1.72 => ( ~ ( member @ A @ X4 @ B4 )
% 3.24/1.72 => ( ( ( insert @ A @ X4 @ A6 )
% 3.24/1.72 = ( insert @ A @ X4 @ B4 ) )
% 3.24/1.72 = ( A6 = B4 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_139_Set_Oset__insert,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,A6: set @ A] :
% 3.24/1.72 ( ( member @ A @ X4 @ A6 )
% 3.24/1.72 => ~ ! [B5: set @ A] :
% 3.24/1.72 ( ( A6
% 3.24/1.72 = ( insert @ A @ X4 @ B5 ) )
% 3.24/1.72 => ( member @ A @ X4 @ B5 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_140_insertI2,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 3.24/1.72 ( ( member @ A @ A2 @ B4 )
% 3.24/1.72 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_141_insertI1,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_142_insertE,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B3: A,A6: set @ A] :
% 3.24/1.72 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
% 3.24/1.72 => ( ( A2 != B3 )
% 3.24/1.72 => ( member @ A @ A2 @ A6 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_143_guarded__def,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces1121166967uarded @ A @ B @ C )
% 3.24/1.72 = ( ^ [Sys2: A > ( proces554692349s_term @ B @ C )] :
% 3.24/1.72 ! [X6: A,Y5: C] :
% 3.24/1.72 ( ( Sys2 @ X6 )
% 3.24/1.72 != ( proces1627516585ss_VAR @ C @ B @ Y5 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_144_insert__compr,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( insert @ A )
% 3.24/1.72 = ( ^ [A3: A,B6: set @ A] :
% 3.24/1.72 ( collect @ A
% 3.24/1.72 @ ^ [X: A] :
% 3.24/1.72 ( ( X = A3 )
% 3.24/1.72 | ( member @ A @ X @ B6 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_145_insert__Collect,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,P6: A > $o] :
% 3.24/1.72 ( ( insert @ A @ A2 @ ( collect @ A @ P6 ) )
% 3.24/1.72 = ( collect @ A
% 3.24/1.72 @ ^ [U: A] :
% 3.24/1.72 ( ( U != A2 )
% 3.24/1.72 => ( P6 @ U ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_146_isACT__VAR,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
% 3.24/1.72 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.24/1.72 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X5 ) )
% 3.24/1.72 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_147_isACT_Oelims_I2_J,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ~ ( proces10484146Action @ D @ P4 ) )
% 3.24/1.72 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 != ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_148_isACT_Oelims_I3_J,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( proces10484146Action @ D @ P4 ) )
% 3.24/1.72 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_149_CH2_Oelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 3.24/1.72 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( Y != T23 ) )
% 3.24/1.72 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_150_CH1_Oelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 3.24/1.72 => ( ! [T12: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ? [T23: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( Y != T12 ) )
% 3.24/1.72 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_151_process__term_Oinject_I4_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 3.24/1.72 = ( ( X41 = Y41 )
% 3.24/1.72 & ( X42 = Y42 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_152_process__term_Oinject_I3_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.24/1.72 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 3.24/1.72 = ( ( X31 = Y31 )
% 3.24/1.72 & ( X32 = Y32 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_153_process__term_Osimps_I47_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.24/1.72 = ( insert @ A @ X31 @ ( proces1264666542s_term @ A @ Pvar @ X32 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_154_process__term_Osimps_I20_J,axiom,
% 3.24/1.72 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.24/1.72 = ( F4 @ X41 @ X42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_155_isACT_Osimps_I4_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T13: proces554692349s_term @ D @ A,T24: proces554692349s_term @ D @ A] :
% 3.24/1.72 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T13 @ T24 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_156_process__term_Osimps_I19_J,axiom,
% 3.24/1.72 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.24/1.72 = ( F3 @ X31 @ X32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_157_isACT_Osimps_I3_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_158_process__term_Odistinct_I11_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.24/1.72 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_159_process__term_Odistinct_I7_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.24/1.72 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_160_process__term_Odistinct_I9_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.24/1.72 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_161_process__term_Oset__intros_I2_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,A1: A,A22: proces554692349s_term @ A @ Pvar] : ( member @ A @ A1 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_162_process__term_Oset__intros_I3_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xa: A,A22: proces554692349s_term @ A @ Pvar,A1: A] :
% 3.24/1.72 ( ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ A22 ) )
% 3.24/1.72 => ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_163_process__term_Oset__intros_I4_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xc2: A,A1a: proces554692349s_term @ A @ Pvar,A2a: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ A1a ) )
% 3.24/1.72 => ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_164_process__term_Oset__intros_I5_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xe: A,A2a: proces554692349s_term @ A @ Pvar,A1a: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ A2a ) )
% 3.24/1.72 => ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_165_process__term_Odistinct_I3_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X14: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 3.24/1.72 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_166_process__term_Odistinct_I5_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X14: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
% 3.24/1.72 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_167_process__term_Osimps_I27_J,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ C @ ( F1 @ X31 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X32 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_168_process__term_Osimps_I28_J,axiom,
% 3.24/1.72 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.24/1.72 = ( proces89589571ess_CH @ B @ C @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X41 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X42 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_169_process__term_Oexhaust,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Y: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ! [X13: Pvar] :
% 3.24/1.72 ( Y
% 3.24/1.72 != ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 3.24/1.72 => ( ! [X24: proces634752977rocess @ A] :
% 3.24/1.72 ( Y
% 3.24/1.72 != ( proces1062592052s_PROC @ A @ Pvar @ X24 ) )
% 3.24/1.72 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( Y
% 3.24/1.72 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 3.24/1.72 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( Y
% 3.24/1.72 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_170_process__term_Oinduct,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,P6: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ! [X3: Pvar] : ( P6 @ ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
% 3.24/1.72 => ( ! [X3: proces634752977rocess @ A] : ( P6 @ ( proces1062592052s_PROC @ A @ Pvar @ X3 ) )
% 3.24/1.72 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( P6 @ X2a )
% 3.24/1.72 => ( P6 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 3.24/1.72 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( P6 @ X1a )
% 3.24/1.72 => ( ( P6 @ X2a )
% 3.24/1.72 => ( P6 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 3.24/1.72 => ( P6 @ Process_term ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_171_isACT_Oinduct,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,P6: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_172_PREF_Oinduct,axiom,
% 3.24/1.72 ! [C: $tType,A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_173_CONT_Oinduct,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_174_CH2_Oinduct,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,P6: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( P6 @ A0 @ A1 ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_175_CH1_Osimps_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
% 3.24/1.72 = T13 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_176_CH2_Osimps_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
% 3.24/1.72 = T24 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_177_CONT_Osimps_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.24/1.72 = T2 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_178_PREF_Osimps_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.24/1.72 = A2 ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_179_process__term_Oset__cases_I1_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,E: A,A2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ A2 ) )
% 3.24/1.72 => ( ! [Z3: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1062592052s_PROC @ A @ Pvar @ Z3 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z3 ) ) )
% 3.24/1.72 => ( ! [Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( A2
% 3.24/1.72 != ( proces1454156180ss_ACT @ A @ Pvar @ E @ Z2 ) )
% 3.24/1.72 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) )
% 3.24/1.72 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( A2
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z1 ) ) )
% 3.24/1.72 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_180_isACT_Oelims_I1_J,axiom,
% 3.24/1.72 ! [D: $tType,A: $tType,B: $tType,C: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 3.24/1.72 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 3.24/1.72 => ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 3.24/1.72 => ~ Y )
% 3.24/1.72 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.24/1.72 => Y ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_181_PREF_Oelims,axiom,
% 3.24/1.72 ! [A: $tType,C: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 3.24/1.72 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces460752237s_term @ C @ B @ B
% 3.24/1.72 @ ^ [Aa3: C] : ( undefined @ B )
% 3.24/1.72 @ ( proces745025900prefOf @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces745025900prefOf @ B @ P4 ) ) )
% 3.24/1.72 => ( ! [A4: B] :
% 3.24/1.72 ( ? [T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( Y != A4 ) )
% 3.24/1.72 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( undefined @ B ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_182_CONT_Oelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 3.24/1.72 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( Y != T4 ) )
% 3.24/1.72 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_183_process__term_Orel__cases,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B3: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B3 )
% 3.24/1.72 => ( ! [X3: Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
% 3.24/1.72 => ! [Y6: C] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces1627516585ss_VAR @ C @ B @ Y6 ) )
% 3.24/1.72 => ~ ( R22 @ X3 @ Y6 ) ) )
% 3.24/1.72 => ( ! [Xa2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 3.24/1.72 => ! [Ya2: proces634752977rocess @ B] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ C @ Ya2 ) )
% 3.24/1.72 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya2 ) ) )
% 3.24/1.72 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 3.24/1.72 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 3.24/1.72 => ( ( R1 @ X1a @ Y1a )
% 3.24/1.72 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 3.24/1.72 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 3.24/1.72 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( B3
% 3.24/1.72 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 3.24/1.72 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 3.24/1.72 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_184_process__term_Orel__induct,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X4: proces554692349s_term @ A @ Pvar,Y: proces554692349s_term @ B @ C,Q3: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X4 @ Y )
% 3.24/1.72 => ( ! [A12: Pvar,B1: C] :
% 3.24/1.72 ( ( R22 @ A12 @ B1 )
% 3.24/1.72 => ( Q3 @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 3.24/1.72 => ( ! [A23: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R1 @ A23 @ B22 )
% 3.24/1.72 => ( Q3 @ ( proces1062592052s_PROC @ A @ Pvar @ A23 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 3.24/1.72 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( R1 @ A31 @ B31 )
% 3.24/1.72 => ( ( Q3 @ A32 @ B32 )
% 3.24/1.72 => ( Q3 @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 3.24/1.72 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( Q3 @ A41 @ B41 )
% 3.24/1.72 => ( ( Q3 @ A42 @ B42 )
% 3.24/1.72 => ( Q3 @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 3.24/1.72 => ( Q3 @ X4 @ Y ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_185_isACT_Ocases,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) )
% 3.24/1.72 => ~ ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_186_process__term_Orel__inject_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 3.24/1.72 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.24/1.72 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_187_process__term_Orel__inject_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 3.24/1.72 = ( ( R1 @ X31 @ Y31 )
% 3.24/1.72 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_188_process__term_Orel__intros_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.24/1.72 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 3.24/1.72 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_189_process__term_Orel__intros_I3_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 3.24/1.72 ( ( R1 @ X31 @ Y31 )
% 3.24/1.72 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 3.24/1.72 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_190_process__term_Orel__inject_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y13: C] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) )
% 3.24/1.72 = ( R22 @ X14 @ Y13 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_191_process__term_Orel__intros_I1_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X14: Pvar,Y13: C,R1: A > B > $o] :
% 3.24/1.72 ( ( R22 @ X14 @ Y13 )
% 3.24/1.72 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_192_process__term_Orel__refl,axiom,
% 3.24/1.72 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X4: proces554692349s_term @ C @ D] :
% 3.24/1.72 ( ! [X3: C] : ( R1a @ X3 @ X3 )
% 3.24/1.72 => ( ! [X3: D] : ( R2a @ X3 @ X3 )
% 3.24/1.72 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_193_process__term_Orel__eq,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ A @ B @ B
% 3.24/1.72 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.24/1.72 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) )
% 3.24/1.72 = ( ^ [Y3: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y3 = Z ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_194_process__term_Orel__map_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1b: E2 > C > $o,S2b: F5 > D > $o,I1: A > E2,I2: B > F5,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D] :
% 3.24/1.72 ( ( proces2029722208s_term @ E2 @ C @ F5 @ D @ S1b @ S2b @ ( proces224683037s_term @ A @ E2 @ B @ F5 @ I1 @ I2 @ X4 ) @ Y )
% 3.24/1.72 = ( proces2029722208s_term @ A @ C @ B @ D
% 3.24/1.72 @ ^ [X: A] : ( S1b @ ( I1 @ X ) )
% 3.24/1.72 @ ^ [X: B] : ( S2b @ ( I2 @ X ) )
% 3.24/1.72 @ X4
% 3.24/1.72 @ Y ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_195_process__term_Orel__map_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1a: A > E2 > $o,S2a: B > F5 > $o,X4: proces554692349s_term @ A @ B,G1: C > E2,G2: D > F5,Y: proces554692349s_term @ C @ D] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a @ X4 @ ( proces224683037s_term @ C @ E2 @ D @ F5 @ G1 @ G2 @ Y ) )
% 3.24/1.72 = ( proces2029722208s_term @ A @ C @ B @ D
% 3.24/1.72 @ ^ [X: A,Y4: C] : ( S1a @ X @ ( G1 @ Y4 ) )
% 3.24/1.72 @ ^ [X: B,Y4: D] : ( S2a @ X @ ( G2 @ Y4 ) )
% 3.24/1.72 @ X4
% 3.24/1.72 @ Y ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_196_process__term_Orel__intros_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 3.24/1.72 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 3.24/1.72 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_197_process__term_Orel__inject_I2_J,axiom,
% 3.24/1.72 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 3.24/1.72 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_198_process__term_Orel__distinct_I2_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X14: D] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_199_process__term_Orel__distinct_I1_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y2: proces634752977rocess @ B] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_200_process__term_Orel__distinct_I10_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_201_process__term_Orel__distinct_I9_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_202_process__term_Orel__distinct_I8_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_203_process__term_Orel__distinct_I7_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_204_process__term_Orel__distinct_I6_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X14: D] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_205_process__term_Orel__distinct_I5_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_206_process__term_Orel__distinct_I4_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X14: D] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_207_process__term_Orel__distinct_I3_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_208_process__term_Orel__distinct_I11_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_209_process__term_Orel__distinct_I12_J,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 3.24/1.72 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_210_CH2_Ocases,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 3.24/1.72 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_211_CONT_Ocases,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 3.24/1.72 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_212_PREF_Ocases,axiom,
% 3.24/1.72 ! [C: $tType,A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.24/1.72 ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.24/1.72 => ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 3.24/1.72 => ~ ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( X4
% 3.24/1.72 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_213_CH1_Opelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.24/1.72 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( ( Y = T12 )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.24/1.72 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_214_CH2_Opelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.24/1.72 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( ( Y = T23 )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.24/1.72 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_215_CONT_Opelims,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.24/1.72 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.24/1.72 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( ( Y = T4 )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 3.24/1.72 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_216_PREF_Opelims,axiom,
% 3.24/1.72 ! [C: $tType,A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 3.24/1.72 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ B @ X7 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces460752237s_term @ C @ B @ B
% 3.24/1.72 @ ^ [Aa3: C] : ( undefined @ B )
% 3.24/1.72 @ ( proces745025900prefOf @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 3.24/1.72 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ B] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces745025900prefOf @ B @ P4 ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.24/1.72 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( ( Y = A4 )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 3.24/1.72 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( undefined @ B ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_217_isACT_Opelims_I1_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 3.24/1.72 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 = Y )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( ( Y
% 3.24/1.72 = ( proces10484146Action @ D @ P4 ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 3.24/1.72 => ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 3.24/1.72 => ( Y
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
% 3.24/1.72 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.24/1.72 => ( ~ Y
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_218_isACT_Opelims_I3_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 3.24/1.72 => ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.24/1.72 => ( proces10484146Action @ D @ P4 ) ) )
% 3.24/1.72 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_219_isACT_Opelims_I2_J,axiom,
% 3.24/1.72 ! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ Xa ) )
% 3.24/1.72 => ( ! [X7: A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1627516585ss_VAR @ A @ D @ X7 ) )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
% 3.24/1.72 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.24/1.72 @ ^ [Pvar2: C] : $false
% 3.24/1.72 @ ( proces10484146Action @ B )
% 3.24/1.72 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 3.24/1.72 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.24/1.72 @ ( X4 @ X7 ) ) ) )
% 3.24/1.72 => ( ! [P4: proces634752977rocess @ D] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.24/1.72 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.24/1.72 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 3.24/1.72 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 3.24/1.72 ( ( Xa
% 3.24/1.72 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 3.24/1.72 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_220_pred__equals__eq2,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 3.24/1.72 ( ( ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R ) )
% 3.24/1.72 = ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S ) ) )
% 3.24/1.72 = ( R = S ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_221_process__term_Oset__cases_I2_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,E: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 3.24/1.72 => ( ( A2
% 3.24/1.72 != ( proces1627516585ss_VAR @ Pvar @ A @ E ) )
% 3.24/1.72 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 3.24/1.72 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( A2
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 3.24/1.72 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( A2
% 3.24/1.72 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.24/1.72 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_222_process__term_Oset__intros_I6_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,Ab2: Pvar] : ( member @ Pvar @ Ab2 @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_223_process__term_Oset__intros_I7_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 3.24/1.72 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 3.24/1.72 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_224_process__term_Oset__intros_I8_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 3.24/1.72 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_225_process__term_Oset__intros_I9_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 3.24/1.72 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_226_process__term_Osimps_I51_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.24/1.72 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_227_process__term_Orel__refl__strong,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 3.24/1.72 ( ! [Z1: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( R1a @ Z1 @ Z1 ) )
% 3.24/1.72 => ( ! [Z2: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( R2a @ Z2 @ Z2 ) )
% 3.24/1.72 => ( proces2029722208s_term @ A @ A @ B @ B @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_228_process__term_Orel__mono__strong,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 3.24/1.72 ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
% 3.24/1.72 => ( ! [Z1: A,Y1: C] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Y ) )
% 3.24/1.72 => ( ( R1 @ Z1 @ Y1 )
% 3.24/1.72 => ( R1a @ Z1 @ Y1 ) ) ) )
% 3.24/1.72 => ( ! [Z2: B,Y23: D] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Y ) )
% 3.24/1.72 => ( ( R22 @ Z2 @ Y23 )
% 3.24/1.72 => ( R2a @ Z2 @ Y23 ) ) ) )
% 3.24/1.72 => ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ X4 @ Y ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_229_process__term_Orel__cong,axiom,
% 3.24/1.72 ! [A: $tType,B: $tType,D: $tType,C: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,Xa: proces554692349s_term @ C @ D,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ( Y = Xa )
% 3.24/1.72 => ( ! [Z1: A,Y1: C] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Xa ) )
% 3.24/1.72 => ( ( R1 @ Z1 @ Y1 )
% 3.24/1.72 = ( R1a @ Z1 @ Y1 ) ) ) )
% 3.24/1.72 => ( ! [Z2: B,Y23: D] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Xa ) )
% 3.24/1.72 => ( ( R22 @ Z2 @ Y23 )
% 3.24/1.72 = ( R2a @ Z2 @ Y23 ) ) ) )
% 3.24/1.72 => ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
% 3.24/1.72 = ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_230_process__term_Omap__cong,axiom,
% 3.24/1.72 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ! [Z1: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( F1 @ Z1 )
% 3.24/1.72 = ( G1 @ Z1 ) ) )
% 3.24/1.72 => ( ! [Z2: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( F2 @ Z2 )
% 3.24/1.72 = ( G2 @ Z2 ) ) )
% 3.24/1.72 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 3.24/1.72 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_231_process__term_Omap__cong0,axiom,
% 3.24/1.72 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 3.24/1.72 ( ! [Z1: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( F1 @ Z1 )
% 3.24/1.72 = ( G1 @ Z1 ) ) )
% 3.24/1.72 => ( ! [Z2: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( F2 @ Z2 )
% 3.24/1.72 = ( G2 @ Z2 ) ) )
% 3.24/1.72 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 3.24/1.72 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ X4 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_232_process__term_Oinj__map__strong,axiom,
% 3.24/1.72 ! [C: $tType,D: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Xa: proces554692349s_term @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 3.24/1.72 ( ! [Z1: A,Z1a: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( member @ A @ Z1a @ ( proces1264666542s_term @ A @ B @ Xa ) )
% 3.24/1.72 => ( ( ( F1 @ Z1 )
% 3.24/1.72 = ( F1a @ Z1a ) )
% 3.24/1.72 => ( Z1 = Z1a ) ) ) )
% 3.24/1.72 => ( ! [Z2: B,Z2a: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( member @ B @ Z2a @ ( proces1493547885s_term @ A @ B @ Xa ) )
% 3.24/1.72 => ( ( ( F2 @ Z2 )
% 3.24/1.72 = ( F2a @ Z2a ) )
% 3.24/1.72 => ( Z2 = Z2a ) ) ) )
% 3.24/1.72 => ( ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 3.24/1.72 = ( proces224683037s_term @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 3.24/1.72 => ( X4 = Xa ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_233_process__term_Osimps_I49_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,X14: Pvar] :
% 3.24/1.72 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 3.24/1.72 = ( insert @ Pvar @ X14 @ ( bot_bot @ ( set @ Pvar ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_234_process__term_Opred__mono__strong,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,X4: proces554692349s_term @ A @ B,P1a: A > $o,P2a: B > $o] :
% 3.24/1.72 ( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
% 3.24/1.72 => ( ! [Z1: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( P1 @ Z1 )
% 3.24/1.72 => ( P1a @ Z1 ) ) )
% 3.24/1.72 => ( ! [Z2: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
% 3.24/1.72 => ( ( P22 @ Z2 )
% 3.24/1.72 => ( P2a @ Z2 ) ) )
% 3.24/1.72 => ( proces2118920028s_term @ A @ B @ P1a @ P2a @ X4 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_235_singletonI,axiom,
% 3.24/1.72 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_236_singleton__conv,axiom,
% 3.24/1.72 ! [A: $tType,A2: A] :
% 3.24/1.72 ( ( collect @ A
% 3.24/1.72 @ ^ [X: A] : ( X = A2 ) )
% 3.24/1.72 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_237_singleton__conv2,axiom,
% 3.24/1.72 ! [A: $tType,A2: A] :
% 3.24/1.72 ( ( collect @ A
% 3.24/1.72 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.24/1.72 @ A2 ) )
% 3.24/1.72 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_238_process__term_Opred__inject_I1_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,P1: A > $o,P22: Pvar > $o,A2: Pvar] :
% 3.24/1.72 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 3.24/1.72 = ( P22 @ A2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_239_process__term_Opred__inject_I4_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 3.24/1.72 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ A2 )
% 3.24/1.72 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_240_process__term_Opred__inject_I3_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.24/1.72 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 3.24/1.72 = ( ( P1 @ A2 )
% 3.24/1.72 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_241_process__term_Osimps_I50_J,axiom,
% 3.24/1.72 ! [A: $tType,Pvar: $tType,X2: proces634752977rocess @ A] :
% 3.24/1.72 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.24/1.72 = ( bot_bot @ ( set @ Pvar ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_242_process__term_Omap__cong__pred,axiom,
% 3.24/1.72 ! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ( proces2118920028s_term @ A @ B
% 3.24/1.72 @ ^ [Z12: A] :
% 3.24/1.72 ( ( F1 @ Z12 )
% 3.24/1.72 = ( G1 @ Z12 ) )
% 3.24/1.72 @ ^ [Z22: B] :
% 3.24/1.72 ( ( F2 @ Z22 )
% 3.24/1.72 = ( G2 @ Z22 ) )
% 3.24/1.72 @ Ya )
% 3.24/1.72 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
% 3.24/1.72 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_243_process__term_Osimps_I45_J,axiom,
% 3.24/1.72 ! [Pvar: $tType,A: $tType,X14: Pvar] :
% 3.24/1.72 ( ( proces1264666542s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
% 3.24/1.72 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_244_Collect__conv__if,axiom,
% 3.24/1.72 ! [A: $tType,P6: A > $o,A2: A] :
% 3.24/1.72 ( ( ( P6 @ A2 )
% 3.24/1.72 => ( ( collect @ A
% 3.24/1.72 @ ^ [X: A] :
% 3.24/1.72 ( ( X = A2 )
% 3.24/1.72 & ( P6 @ X ) ) )
% 3.24/1.72 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.24/1.72 & ( ~ ( P6 @ A2 )
% 3.24/1.72 => ( ( collect @ A
% 3.24/1.72 @ ^ [X: A] :
% 3.24/1.72 ( ( X = A2 )
% 3.24/1.72 & ( P6 @ X ) ) )
% 3.24/1.72 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_245_Collect__conv__if2,axiom,
% 3.24/1.72 ! [A: $tType,P6: A > $o,A2: A] :
% 3.24/1.72 ( ( ( P6 @ A2 )
% 3.24/1.72 => ( ( collect @ A
% 3.24/1.72 @ ^ [X: A] :
% 3.24/1.72 ( ( A2 = X )
% 3.24/1.72 & ( P6 @ X ) ) )
% 3.24/1.72 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.24/1.72 & ( ~ ( P6 @ A2 )
% 3.24/1.72 => ( ( collect @ A
% 3.24/1.72 @ ^ [X: A] :
% 3.24/1.72 ( ( A2 = X )
% 3.24/1.72 & ( P6 @ X ) ) )
% 3.24/1.72 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_246_process__term_Opred__True,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType] :
% 3.24/1.72 ( ( proces2118920028s_term @ A @ B
% 3.24/1.72 @ ^ [Uu: A] : $true
% 3.24/1.72 @ ^ [Uu: B] : $true )
% 3.24/1.72 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_247_empty__def,axiom,
% 3.24/1.72 ! [A: $tType] :
% 3.24/1.72 ( ( bot_bot @ ( set @ A ) )
% 3.24/1.72 = ( collect @ A
% 3.24/1.72 @ ^ [X: A] : $false ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_248_singleton__inject,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B3: A] :
% 3.24/1.72 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.24/1.72 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.24/1.72 => ( A2 = B3 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_249_insert__not__empty,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,A6: set @ A] :
% 3.24/1.72 ( ( insert @ A @ A2 @ A6 )
% 3.24/1.72 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_250_doubleton__eq__iff,axiom,
% 3.24/1.72 ! [A: $tType,A2: A,B3: A,C3: A,D2: A] :
% 3.24/1.72 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.24/1.72 = ( insert @ A @ C3 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.24/1.72 = ( ( ( A2 = C3 )
% 3.24/1.72 & ( B3 = D2 ) )
% 3.24/1.72 | ( ( A2 = D2 )
% 3.24/1.72 & ( B3 = C3 ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_251_singleton__iff,axiom,
% 3.24/1.72 ! [A: $tType,B3: A,A2: A] :
% 3.24/1.72 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.24/1.72 = ( B3 = A2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_252_singletonD,axiom,
% 3.24/1.72 ! [A: $tType,B3: A,A2: A] :
% 3.24/1.72 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.24/1.72 => ( B3 = A2 ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_253_process__term_Opred__cong,axiom,
% 3.24/1.72 ! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 3.24/1.72 ( ( X4 = Ya )
% 3.24/1.72 => ( ! [Z1: A] :
% 3.24/1.72 ( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( P1 @ Z1 )
% 3.24/1.72 = ( P1a @ Z1 ) ) )
% 3.24/1.72 => ( ! [Z2: B] :
% 3.24/1.72 ( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
% 3.24/1.72 => ( ( P22 @ Z2 )
% 3.24/1.72 = ( P2a @ Z2 ) ) )
% 3.24/1.72 => ( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
% 3.24/1.72 = ( proces2118920028s_term @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(fact_254_the__elem__eq,axiom,
% 3.24/1.72 ! [A: $tType,X4: A] :
% 3.24/1.72 ( ( the_elem @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.24/1.72 = X4 ) ).
% 3.24/1.72
% 3.24/1.72 thf(help_If_3_1_T,axiom,
% 3.24/1.72 ! [P6: $o] :
% 3.24/1.72 ( ( P6 = $true )
% 3.24/1.72 | ( P6 = $false ) ) ).
% 3.24/1.72
% 3.24/1.72 thf(help_If_2_1_T,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,Y: A] :
% 3.24/1.72 ( ( if @ A @ $false @ X4 @ Y )
% 3.24/1.72 = Y ) ).
% 3.24/1.72
% 3.24/1.72 thf(help_If_1_1_T,axiom,
% 3.24/1.72 ! [A: $tType,X4: A,Y: A] :
% 3.24/1.72 ( ( if @ A @ $true @ X4 @ Y )
% 3.24/1.72 = X4 ) ).
% 3.24/1.72
% 3.24/1.72 thf(conj_0,conjecture,
% 3.24/1.72 ( ( ( proces10484146Action @ a @ pa )
% 3.24/1.72 = ( proces10484146Action @ a @ p2 ) )
% 3.24/1.72 & ( ( proces401113213Choice @ a @ pa )
% 3.24/1.72 = ( proces401113213Choice @ a @ p2 ) ) ) ).
% 3.24/1.72 ------------------------
% 3.24/1.75 % (1507)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/183Mi)
% 3.24/1.75 % (1508)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/4Mi)
% 3.24/1.75 % (1510)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/2Mi)
% 3.24/1.75 % (1512)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/275Mi)
% 3.24/1.75 % (1509)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/27Mi)
% 3.24/1.75 % (1511)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/2Mi)
% 3.24/1.75 % (1513)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/18Mi)
% 3.24/1.76 % (1510)Instruction limit reached!
% 3.24/1.76 % (1510)------------------------------
% 3.24/1.76 % (1510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.76 % (1510)Termination reason: Unknown
% 3.24/1.76 % (1511)Instruction limit reached!
% 3.24/1.76 % (1511)------------------------------
% 3.24/1.76 % (1511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.76 % (1510)Termination phase: shuffling
% 3.24/1.76
% 3.24/1.76 % (1510)Memory used [KB]: 1535
% 3.24/1.76 % (1510)Time elapsed: 0.003 s
% 3.24/1.76 % (1510)Instructions burned: 2 (million)
% 3.24/1.76 % (1510)------------------------------
% 3.24/1.76 % (1510)------------------------------
% 3.24/1.76 % (1511)Termination reason: Unknown
% 3.24/1.76 % (1511)Termination phase: shuffling
% 3.24/1.76
% 3.24/1.76 % (1511)Memory used [KB]: 1535
% 3.24/1.76 % (1511)Time elapsed: 0.003 s
% 3.24/1.76 % (1511)Instructions burned: 2 (million)
% 3.24/1.76 % (1511)------------------------------
% 3.24/1.76 % (1511)------------------------------
% 3.24/1.76 % (1508)Instruction limit reached!
% 3.24/1.76 % (1508)------------------------------
% 3.24/1.76 % (1508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.76 % (1508)Termination reason: Unknown
% 3.24/1.76 % (1508)Termination phase: shuffling
% 3.24/1.76
% 3.24/1.76 % (1508)Memory used [KB]: 1535
% 3.24/1.76 % (1508)Time elapsed: 0.004 s
% 3.24/1.76 % (1508)Instructions burned: 4 (million)
% 3.24/1.76 % (1508)------------------------------
% 3.24/1.76 % (1508)------------------------------
% 3.24/1.76 % (1513)Instruction limit reached!
% 3.24/1.76 % (1513)------------------------------
% 3.24/1.76 % (1513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.76 % (1513)Termination reason: Unknown
% 3.24/1.76 % (1513)Termination phase: shuffling
% 3.24/1.76
% 3.24/1.76 % (1513)Memory used [KB]: 1918
% 3.24/1.76 % (1513)Time elapsed: 0.011 s
% 3.24/1.76 % (1513)Instructions burned: 18 (million)
% 3.24/1.76 % (1513)------------------------------
% 3.24/1.76 % (1513)------------------------------
% 3.24/1.77 % (1509)Instruction limit reached!
% 3.24/1.77 % (1509)------------------------------
% 3.24/1.77 % (1509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.77 % (1509)Termination reason: Unknown
% 3.24/1.77 % (1509)Termination phase: shuffling
% 3.24/1.77
% 3.24/1.77 % (1509)Memory used [KB]: 2046
% 3.24/1.77 % (1509)Time elapsed: 0.016 s
% 3.24/1.77 % (1509)Instructions burned: 28 (million)
% 3.24/1.77 % (1509)------------------------------
% 3.24/1.77 % (1509)------------------------------
% 3.24/1.77 % (1515)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/37Mi)
% 3.24/1.77 % (1514)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/3Mi)
% 3.24/1.77 % (1516)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/15Mi)
% 3.24/1.77 % (1514)Instruction limit reached!
% 3.24/1.77 % (1514)------------------------------
% 3.24/1.77 % (1514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.77 % (1514)Termination reason: Unknown
% 3.24/1.77 % (1514)Termination phase: shuffling
% 3.24/1.77
% 3.24/1.77 % (1514)Memory used [KB]: 1535
% 3.24/1.77 % (1514)Time elapsed: 0.004 s
% 3.24/1.77 % (1514)Instructions burned: 4 (million)
% 3.24/1.77 % (1514)------------------------------
% 3.24/1.77 % (1514)------------------------------
% 3.24/1.78 % (1516)Instruction limit reached!
% 3.24/1.78 % (1516)------------------------------
% 3.24/1.78 % (1516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.78 % (1516)Termination reason: Unknown
% 3.24/1.78 % (1516)Termination phase: shuffling
% 3.24/1.78
% 3.24/1.78 % (1516)Memory used [KB]: 1791
% 3.24/1.78 % (1516)Time elapsed: 0.009 s
% 3.24/1.78 % (1516)Instructions burned: 16 (million)
% 3.24/1.78 % (1516)------------------------------
% 3.24/1.78 % (1516)------------------------------
% 3.24/1.78 % (1517)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/3Mi)
% 3.24/1.78 % (1517)Instruction limit reached!
% 3.24/1.78 % (1517)------------------------------
% 3.24/1.78 % (1517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.78 % (1517)Termination reason: Unknown
% 3.24/1.78 % (1517)Termination phase: shuffling
% 3.24/1.78
% 3.24/1.78 % (1517)Memory used [KB]: 1535
% 3.24/1.78 % (1517)Time elapsed: 0.004 s
% 3.24/1.78 % (1517)Instructions burned: 3 (million)
% 3.24/1.78 % (1517)------------------------------
% 3.24/1.78 % (1517)------------------------------
% 3.24/1.79 % (1518)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/1041Mi)
% 3.24/1.79 % (1515)Instruction limit reached!
% 3.24/1.79 % (1515)------------------------------
% 3.24/1.79 % (1515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.79 % (1515)Termination reason: Unknown
% 3.24/1.79 % (1515)Termination phase: shuffling
% 3.24/1.79
% 3.24/1.79 % (1515)Memory used [KB]: 2302
% 3.24/1.79 % (1515)Time elapsed: 0.019 s
% 3.24/1.79 % (1515)Instructions burned: 37 (million)
% 3.24/1.79 % (1515)------------------------------
% 3.24/1.79 % (1515)------------------------------
% 3.24/1.79 % (1519)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/7Mi)
% 3.27/1.80 % (1520)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/16Mi)
% 3.27/1.80 % (1519)Instruction limit reached!
% 3.27/1.80 % (1519)------------------------------
% 3.27/1.80 % (1519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (1519)Termination reason: Unknown
% 3.27/1.80 % (1519)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (1519)Memory used [KB]: 1663
% 3.27/1.80 % (1519)Time elapsed: 0.006 s
% 3.27/1.80 % (1519)Instructions burned: 8 (million)
% 3.27/1.80 % (1519)------------------------------
% 3.27/1.80 % (1519)------------------------------
% 3.27/1.80 % (1521)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/3Mi)
% 3.27/1.80 % (1521)Instruction limit reached!
% 3.27/1.80 % (1521)------------------------------
% 3.27/1.80 % (1521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (1521)Termination reason: Unknown
% 3.27/1.80 % (1521)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (1521)Memory used [KB]: 1535
% 3.27/1.80 % (1521)Time elapsed: 0.003 s
% 3.27/1.80 % (1521)Instructions burned: 3 (million)
% 3.27/1.80 % (1521)------------------------------
% 3.27/1.80 % (1521)------------------------------
% 3.27/1.80 % (1507)Instruction limit reached!
% 3.27/1.80 % (1507)------------------------------
% 3.27/1.80 % (1507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (1507)Termination reason: Unknown
% 3.27/1.80 % (1507)Termination phase: Equality resolution with deletion
% 3.27/1.80
% 3.27/1.80 % (1507)Memory used [KB]: 3582
% 3.27/1.80 % (1507)Time elapsed: 0.057 s
% 3.27/1.80 % (1507)Instructions burned: 186 (million)
% 3.27/1.80 % (1507)------------------------------
% 3.27/1.80 % (1507)------------------------------
% 3.27/1.80 % (1520)Instruction limit reached!
% 3.27/1.80 % (1520)------------------------------
% 3.27/1.80 % (1520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (1520)Termination reason: Unknown
% 3.27/1.80 % (1520)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (1520)Memory used [KB]: 1918
% 3.27/1.80 % (1520)Time elapsed: 0.010 s
% 3.27/1.80 % (1520)Instructions burned: 16 (million)
% 3.27/1.80 % (1520)------------------------------
% 3.27/1.80 % (1520)------------------------------
% 3.27/1.81 % (1522)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/3Mi)
% 3.27/1.81 % (1522)Instruction limit reached!
% 3.27/1.81 % (1522)------------------------------
% 3.27/1.81 % (1522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.81 % (1522)Termination reason: Unknown
% 3.27/1.81 % (1522)Termination phase: shuffling
% 3.27/1.81
% 3.27/1.81 % (1522)Memory used [KB]: 1535
% 3.27/1.81 % (1522)Time elapsed: 0.004 s
% 3.27/1.81 % (1522)Instructions burned: 4 (million)
% 3.27/1.81 % (1522)------------------------------
% 3.27/1.81 % (1522)------------------------------
% 3.27/1.81 % (1512)Refutation not found, incomplete strategy
% 3.27/1.81 % (1512)------------------------------
% 3.27/1.81 % (1512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.81 % (1512)Termination reason: Refutation not found, incomplete strategy
% 3.27/1.81
% 3.27/1.81
% 3.27/1.81 % (1512)Memory used [KB]: 7419
% 3.27/1.81 % (1512)Time elapsed: 0.058 s
% 3.27/1.81 % (1512)Instructions burned: 114 (million)
% 3.27/1.81 % (1512)------------------------------
% 3.27/1.81 % (1512)------------------------------
% 3.27/1.81 % (1523)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/7Mi)
% 3.27/1.81 % (1525)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/4Mi)
% 3.27/1.82 % (1525)Instruction limit reached!
% 3.27/1.82 % (1525)------------------------------
% 3.27/1.82 % (1525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.82 % (1525)Termination reason: Unknown
% 3.27/1.82 % (1525)Termination phase: shuffling
% 3.27/1.82
% 3.27/1.82 % (1525)Memory used [KB]: 1535
% 3.27/1.82 % (1525)Time elapsed: 0.003 s
% 3.27/1.82 % (1525)Instructions burned: 6 (million)
% 3.27/1.82 % (1525)------------------------------
% 3.27/1.82 % (1525)------------------------------
% 3.27/1.82 % (1524)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/3Mi)
% 3.27/1.82 % (1523)Instruction limit reached!
% 3.27/1.82 % (1523)------------------------------
% 3.27/1.82 % (1523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.82 % (1523)Termination reason: Unknown
% 3.27/1.82 % (1523)Termination phase: shuffling
% 3.27/1.82
% 3.27/1.82 % (1523)Memory used [KB]: 1663
% 3.27/1.82 % (1523)Time elapsed: 0.005 s
% 3.27/1.82 % (1523)Instructions burned: 7 (million)
% 3.27/1.82 % (1523)------------------------------
% 3.27/1.82 % (1523)------------------------------
% 3.27/1.82 % (1524)Instruction limit reached!
% 3.27/1.82 % (1524)------------------------------
% 3.27/1.82 % (1524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.82 % (1524)Termination reason: Unknown
% 3.27/1.82 % (1524)Termination phase: shuffling
% 3.27/1.82
% 3.27/1.82 % (1524)Memory used [KB]: 1535
% 3.27/1.82 % (1524)Time elapsed: 0.003 s
% 3.27/1.82 % (1524)Instructions burned: 3 (million)
% 3.27/1.82 % (1524)------------------------------
% 3.27/1.82 % (1524)------------------------------
% 3.27/1.82 % (1526)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/18Mi)
% 3.27/1.82 % (1527)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/710Mi)
% 3.27/1.82 % (1529)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/902Mi)
% 3.27/1.83 % (1528)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/6Mi)
% 3.27/1.83 % (1526)Instruction limit reached!
% 3.27/1.83 % (1526)------------------------------
% 3.27/1.83 % (1526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.83 % (1526)Termination reason: Unknown
% 3.27/1.83 % (1526)Termination phase: shuffling
% 3.27/1.83
% 3.27/1.83 % (1526)Memory used [KB]: 1918
% 3.27/1.83 % (1526)Time elapsed: 0.011 s
% 3.27/1.83 % (1526)Instructions burned: 19 (million)
% 3.27/1.83 % (1526)------------------------------
% 3.27/1.83 % (1526)------------------------------
% 3.27/1.83 % (1528)Instruction limit reached!
% 3.27/1.83 % (1528)------------------------------
% 3.27/1.83 % (1528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.83 % (1528)Termination reason: Unknown
% 3.27/1.83 % (1528)Termination phase: shuffling
% 3.27/1.83
% 3.27/1.83 % (1528)Memory used [KB]: 1535
% 3.27/1.83 % (1528)Time elapsed: 0.005 s
% 3.27/1.83 % (1528)Instructions burned: 7 (million)
% 3.27/1.83 % (1528)------------------------------
% 3.27/1.83 % (1528)------------------------------
% 3.27/1.83 % (1530)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/21Mi)
% 3.27/1.83 % (1531)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/5Mi)
% 3.27/1.84 % (1531)Instruction limit reached!
% 3.27/1.84 % (1531)------------------------------
% 3.27/1.84 % (1531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.84 % (1531)Termination reason: Unknown
% 3.27/1.84 % (1531)Termination phase: shuffling
% 3.27/1.84
% 3.27/1.84 % (1531)Memory used [KB]: 1535
% 3.27/1.84 % (1531)Time elapsed: 0.004 s
% 3.27/1.84 % (1531)Instructions burned: 5 (million)
% 3.27/1.84 % (1531)------------------------------
% 3.27/1.84 % (1531)------------------------------
% 3.27/1.84 % (1530)Instruction limit reached!
% 3.27/1.84 % (1530)------------------------------
% 3.27/1.84 % (1530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.84 % (1530)Termination reason: Unknown
% 3.27/1.84 % (1530)Termination phase: shuffling
% 3.27/1.84
% 3.27/1.84 % (1530)Memory used [KB]: 1918
% 3.27/1.84 % (1530)Time elapsed: 0.012 s
% 3.27/1.84 % (1530)Instructions burned: 21 (million)
% 3.27/1.84 % (1530)------------------------------
% 3.27/1.84 % (1530)------------------------------
% 3.27/1.85 % (1532)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1352 for (2999ds/6Mi)
% 3.27/1.85 % (1533)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/377Mi)
% 3.27/1.85 % (1532)Instruction limit reached!
% 3.27/1.85 % (1532)------------------------------
% 3.27/1.85 % (1532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.85 % (1532)Termination reason: Unknown
% 3.27/1.85 % (1532)Termination phase: shuffling
% 3.27/1.85
% 3.27/1.85 % (1532)Memory used [KB]: 1663
% 3.27/1.85 % (1532)Time elapsed: 0.005 s
% 3.27/1.85 % (1532)Instructions burned: 6 (million)
% 3.27/1.85 % (1532)------------------------------
% 3.27/1.85 % (1532)------------------------------
% 3.27/1.86 % (1535)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/19Mi)
% 3.27/1.86 % (1534)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/779Mi)
% 3.27/1.87 % (1536)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/879Mi)
% 3.27/1.87 % (1535)Instruction limit reached!
% 3.27/1.87 % (1535)------------------------------
% 3.27/1.87 % (1535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.87 % (1535)Termination reason: Unknown
% 3.27/1.87 % (1535)Termination phase: shuffling
% 3.27/1.87
% 3.27/1.87 % (1535)Memory used [KB]: 2046
% 3.27/1.87 % (1535)Time elapsed: 0.012 s
% 3.27/1.87 % (1535)Instructions burned: 20 (million)
% 3.27/1.87 % (1535)------------------------------
% 3.27/1.87 % (1535)------------------------------
% 3.27/1.89 % (1537)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/17Mi)
% 3.27/1.90 % (1537)Instruction limit reached!
% 3.27/1.90 % (1537)------------------------------
% 3.27/1.90 % (1537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.90 % (1537)Termination reason: Unknown
% 3.27/1.90 % (1537)Termination phase: shuffling
% 3.27/1.90
% 3.27/1.90 % (1537)Memory used [KB]: 1918
% 3.27/1.90 % (1537)Time elapsed: 0.011 s
% 3.27/1.90 % (1537)Instructions burned: 18 (million)
% 3.27/1.90 % (1537)------------------------------
% 3.27/1.90 % (1537)------------------------------
% 3.27/1.91 % (1538)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/3Mi)
% 3.27/1.91 % (1538)Instruction limit reached!
% 3.27/1.91 % (1538)------------------------------
% 3.27/1.91 % (1538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.91 % (1538)Termination reason: Unknown
% 3.27/1.91 % (1538)Termination phase: shuffling
% 3.27/1.91
% 3.27/1.91 % (1538)Memory used [KB]: 1535
% 3.27/1.91 % (1538)Time elapsed: 0.004 s
% 3.27/1.91 % (1538)Instructions burned: 3 (million)
% 3.27/1.91 % (1538)------------------------------
% 3.27/1.91 % (1538)------------------------------
% 3.27/1.93 % (1539)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1352 for (2998ds/30Mi)
% 3.27/1.95 % (1539)Instruction limit reached!
% 3.27/1.95 % (1539)------------------------------
% 3.27/1.95 % (1539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.95 % (1539)Termination reason: Unknown
% 3.27/1.95 % (1539)Termination phase: shuffling
% 3.27/1.95
% 3.27/1.95 % (1539)Memory used [KB]: 2046
% 3.27/1.95 % (1539)Time elapsed: 0.017 s
% 3.27/1.95 % (1539)Instructions burned: 30 (million)
% 3.27/1.95 % (1539)------------------------------
% 3.27/1.95 % (1539)------------------------------
% 3.27/1.96 % (1540)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1352 for (2997ds/127Mi)
% 5.10/2.03 % (1540)Instruction limit reached!
% 5.10/2.03 % (1540)------------------------------
% 5.10/2.03 % (1540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.10/2.03 % (1540)Termination reason: Unknown
% 5.10/2.03 % (1540)Termination phase: Preprocessing 3
% 5.10/2.03
% 5.10/2.03 % (1540)Memory used [KB]: 3326
% 5.10/2.03 % (1540)Time elapsed: 0.065 s
% 5.10/2.03 % (1540)Instructions burned: 127 (million)
% 5.10/2.03 % (1540)------------------------------
% 5.10/2.03 % (1540)------------------------------
% 5.10/2.03 % (1533)Instruction limit reached!
% 5.10/2.03 % (1533)------------------------------
% 5.10/2.03 % (1533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.10/2.03 % (1533)Termination reason: Unknown
% 5.10/2.03 % (1533)Termination phase: Saturation
% 5.10/2.03
% 5.10/2.03 % (1533)Memory used [KB]: 9083
% 5.10/2.03 % (1533)Time elapsed: 0.181 s
% 5.10/2.03 % (1533)Instructions burned: 378 (million)
% 5.10/2.03 % (1533)------------------------------
% 5.10/2.03 % (1533)------------------------------
% 5.10/2.04 % (1541)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/100Mi)
% 5.10/2.04 % (1542)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/3Mi)
% 5.10/2.05 % (1542)Instruction limit reached!
% 5.10/2.05 % (1542)------------------------------
% 5.10/2.05 % (1542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.10/2.05 % (1542)Termination reason: Unknown
% 5.10/2.05 % (1542)Termination phase: shuffling
% 5.10/2.05
% 5.10/2.05 % (1542)Memory used [KB]: 1535
% 5.10/2.05 % (1542)Time elapsed: 0.004 s
% 5.10/2.05 % (1542)Instructions burned: 4 (million)
% 5.10/2.05 % (1542)------------------------------
% 5.10/2.05 % (1542)------------------------------
% 5.10/2.06 % (1543)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/20Mi)
% 5.10/2.07 % (1543)Instruction limit reached!
% 5.10/2.07 % (1543)------------------------------
% 5.10/2.07 % (1543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.10/2.07 % (1543)Termination reason: Unknown
% 5.10/2.07 % (1543)Termination phase: shuffling
% 5.10/2.07
% 5.10/2.07 % (1543)Memory used [KB]: 1918
% 5.10/2.07 % (1543)Time elapsed: 0.013 s
% 5.10/2.07 % (1543)Instructions burned: 21 (million)
% 5.10/2.07 % (1543)------------------------------
% 5.10/2.07 % (1543)------------------------------
% 5.10/2.09 % (1541)Instruction limit reached!
% 5.10/2.09 % (1541)------------------------------
% 5.10/2.09 % (1541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.10/2.09 % (1541)Termination reason: Unknown
% 5.10/2.09 % (1541)Termination phase: Property scanning
% 5.10/2.09
% 5.10/2.09 % (1541)Memory used [KB]: 2942
% 5.10/2.09 % (1541)Time elapsed: 0.048 s
% 5.10/2.09 % (1541)Instructions burned: 100 (million)
% 5.10/2.09 % (1541)------------------------------
% 5.10/2.09 % (1541)------------------------------
% 5.10/2.09 % (1544)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/86Mi)
% 5.10/2.11 % (1545)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/107Mi)
% 5.76/2.12 % (1529)Instruction limit reached!
% 5.76/2.12 % (1529)------------------------------
% 5.76/2.12 % (1529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.12 % (1529)Termination reason: Unknown
% 5.76/2.12 % (1529)Termination phase: Saturation
% 5.76/2.12
% 5.76/2.12 % (1529)Memory used [KB]: 9722
% 5.76/2.12 % (1529)Time elapsed: 0.293 s
% 5.76/2.12 % (1529)Instructions burned: 903 (million)
% 5.76/2.12 % (1529)------------------------------
% 5.76/2.12 % (1529)------------------------------
% 5.76/2.13 % (1547)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_1352 for (2996ds/39Mi)
% 5.76/2.13 % (1544)Instruction limit reached!
% 5.76/2.13 % (1544)------------------------------
% 5.76/2.13 % (1544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.13 % (1544)Termination reason: Unknown
% 5.76/2.13 % (1544)Termination phase: Preprocessing 2
% 5.76/2.13
% 5.76/2.13 % (1544)Memory used [KB]: 2814
% 5.76/2.13 % (1544)Time elapsed: 0.044 s
% 5.76/2.13 % (1544)Instructions burned: 87 (million)
% 5.76/2.13 % (1544)------------------------------
% 5.76/2.13 % (1544)------------------------------
% 5.76/2.14 % (1547)Instruction limit reached!
% 5.76/2.14 % (1547)------------------------------
% 5.76/2.14 % (1547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.14 % (1547)Termination reason: Unknown
% 5.76/2.14 % (1547)Termination phase: shuffling
% 5.76/2.14
% 5.76/2.14 % (1547)Memory used [KB]: 2302
% 5.76/2.14 % (1547)Time elapsed: 0.013 s
% 5.76/2.14 % (1547)Instructions burned: 39 (million)
% 5.76/2.14 % (1547)------------------------------
% 5.76/2.14 % (1547)------------------------------
% 5.76/2.15 % (1550)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/46Mi)
% 5.76/2.15 % (1549)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/448Mi)
% 5.76/2.16 % (1550)Instruction limit reached!
% 5.76/2.16 % (1550)------------------------------
% 5.76/2.16 % (1550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.16 % (1550)Termination reason: Unknown
% 5.76/2.16 % (1550)Termination phase: shuffling
% 5.76/2.16
% 5.76/2.16 % (1550)Memory used [KB]: 2430
% 5.76/2.16 % (1550)Time elapsed: 0.017 s
% 5.76/2.16 % (1550)Instructions burned: 48 (million)
% 5.76/2.16 % (1550)------------------------------
% 5.76/2.16 % (1550)------------------------------
% 5.76/2.17 % (1545)Instruction limit reached!
% 5.76/2.17 % (1545)------------------------------
% 5.76/2.17 % (1545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.17 % (1545)Termination reason: Unknown
% 5.76/2.17 % (1545)Termination phase: Preprocessing 3
% 5.76/2.17
% 5.76/2.17 % (1545)Memory used [KB]: 3070
% 5.76/2.17 % (1545)Time elapsed: 0.055 s
% 5.76/2.17 % (1545)Instructions burned: 108 (million)
% 5.76/2.17 % (1545)------------------------------
% 5.76/2.17 % (1545)------------------------------
% 5.76/2.17 % (1527)Instruction limit reached!
% 5.76/2.17 % (1527)------------------------------
% 5.76/2.17 % (1527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.17 % (1527)Termination reason: Unknown
% 5.76/2.17 % (1527)Termination phase: Saturation
% 5.76/2.17
% 5.76/2.17 % (1527)Memory used [KB]: 8827
% 5.76/2.17 % (1527)Time elapsed: 0.348 s
% 5.76/2.17 % (1527)Instructions burned: 710 (million)
% 5.76/2.17 % (1527)------------------------------
% 5.76/2.17 % (1527)------------------------------
% 5.76/2.17 % (1551)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/98Mi)
% 5.76/2.18 % (1552)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/507Mi)
% 5.76/2.19 % (1553)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/149Mi)
% 6.24/2.22 % (1534)Instruction limit reached!
% 6.24/2.22 % (1534)------------------------------
% 6.24/2.22 % (1534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.22 % (1534)Termination reason: Unknown
% 6.24/2.22 % (1534)Termination phase: Saturation
% 6.24/2.22
% 6.24/2.22 % (1534)Memory used [KB]: 9978
% 6.24/2.22 % (1534)Time elapsed: 0.358 s
% 6.24/2.22 % (1534)Instructions burned: 779 (million)
% 6.24/2.22 % (1534)------------------------------
% 6.24/2.22 % (1534)------------------------------
% 6.24/2.22 % (1551)Instruction limit reached!
% 6.24/2.22 % (1551)------------------------------
% 6.24/2.22 % (1551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.22 % (1551)Termination reason: Unknown
% 6.24/2.22 % (1551)Termination phase: Property scanning
% 6.24/2.22
% 6.24/2.22 % (1551)Memory used [KB]: 2942
% 6.24/2.22 % (1551)Time elapsed: 0.044 s
% 6.24/2.22 % (1551)Instructions burned: 99 (million)
% 6.24/2.22 % (1551)------------------------------
% 6.24/2.22 % (1551)------------------------------
% 6.24/2.24 % (1554)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/39Mi)
% 6.24/2.25 % (1555)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1352 for (2995ds/6Mi)
% 6.24/2.25 % (1555)Instruction limit reached!
% 6.24/2.25 % (1555)------------------------------
% 6.24/2.25 % (1555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.25 % (1555)Termination reason: Unknown
% 6.24/2.25 % (1555)Termination phase: shuffling
% 6.24/2.25
% 6.24/2.25 % (1555)Memory used [KB]: 1663
% 6.24/2.25 % (1555)Time elapsed: 0.005 s
% 6.24/2.25 % (1555)Instructions burned: 6 (million)
% 6.24/2.25 % (1555)------------------------------
% 6.24/2.25 % (1555)------------------------------
% 6.24/2.25 % (1554)Instruction limit reached!
% 6.24/2.25 % (1554)------------------------------
% 6.24/2.25 % (1554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.25 % (1554)Termination reason: Unknown
% 6.24/2.25 % (1554)Termination phase: shuffling
% 6.24/2.25
% 6.24/2.25 % (1554)Memory used [KB]: 2174
% 6.24/2.25 % (1554)Time elapsed: 0.021 s
% 6.24/2.25 % (1554)Instructions burned: 39 (million)
% 6.24/2.25 % (1554)------------------------------
% 6.24/2.25 % (1554)------------------------------
% 6.24/2.26 % (1553)Instruction limit reached!
% 6.24/2.26 % (1553)------------------------------
% 6.24/2.26 % (1553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.26 % (1553)Termination reason: Unknown
% 6.24/2.26 % (1553)Termination phase: Property scanning
% 6.24/2.26
% 6.24/2.26 % (1553)Memory used [KB]: 3454
% 6.24/2.26 % (1553)Time elapsed: 0.073 s
% 6.24/2.26 % (1553)Instructions burned: 150 (million)
% 6.24/2.26 % (1553)------------------------------
% 6.24/2.26 % (1553)------------------------------
% 6.24/2.27 % (1556)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/1087Mi)
% 6.24/2.28 % (1558)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/44Mi)
% 6.24/2.28 % (1557)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/47Mi)
% 6.24/2.29 % (1536)Instruction limit reached!
% 6.24/2.29 % (1536)------------------------------
% 6.24/2.29 % (1536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.29 % (1536)Termination reason: Unknown
% 6.24/2.29 % (1536)Termination phase: Saturation
% 6.24/2.29
% 6.24/2.29 % (1536)Memory used [KB]: 9083
% 6.24/2.29 % (1536)Time elapsed: 0.448 s
% 6.24/2.29 % (1536)Instructions burned: 879 (million)
% 6.24/2.29 % (1536)------------------------------
% 6.24/2.29 % (1536)------------------------------
% 6.24/2.29 % (1518)Instruction limit reached!
% 6.24/2.29 % (1518)------------------------------
% 6.24/2.29 % (1518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.29 % (1518)Termination reason: Unknown
% 6.24/2.29 % (1518)Termination phase: Saturation
% 6.24/2.29
% 6.24/2.29 % (1518)Memory used [KB]: 11513
% 6.24/2.29 % (1518)Time elapsed: 0.510 s
% 6.24/2.29 % (1518)Instructions burned: 1041 (million)
% 6.24/2.29 % (1518)------------------------------
% 6.24/2.29 % (1518)------------------------------
% 6.69/2.30 % (1558)Instruction limit reached!
% 6.69/2.30 % (1558)------------------------------
% 6.69/2.30 % (1558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.30 % (1558)Termination reason: Unknown
% 6.69/2.30 % (1558)Termination phase: shuffling
% 6.69/2.30
% 6.69/2.30 % (1558)Memory used [KB]: 2302
% 6.69/2.30 % (1558)Time elapsed: 0.022 s
% 6.69/2.30 % (1558)Instructions burned: 44 (million)
% 6.69/2.30 % (1558)------------------------------
% 6.69/2.30 % (1558)------------------------------
% 6.69/2.31 % (1557)Instruction limit reached!
% 6.69/2.31 % (1557)------------------------------
% 6.69/2.31 % (1557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.31 % (1557)Termination reason: Unknown
% 6.69/2.31 % (1557)Termination phase: shuffling
% 6.69/2.31
% 6.69/2.31 % (1557)Memory used [KB]: 2430
% 6.69/2.31 % (1557)Time elapsed: 0.025 s
% 6.69/2.31 % (1557)Instructions burned: 48 (million)
% 6.69/2.31 % (1557)------------------------------
% 6.69/2.31 % (1557)------------------------------
% 6.69/2.31 % (1560)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/62Mi)
% 6.69/2.31 % (1559)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/432Mi)
% 6.69/2.31 % (1561)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/31Mi)
% 6.69/2.32 % (1562)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1352 for (2994ds/96Mi)
% 6.69/2.33 % (1561)Instruction limit reached!
% 6.69/2.33 % (1561)------------------------------
% 6.69/2.33 % (1561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.33 % (1561)Termination reason: Unknown
% 6.69/2.33 % (1561)Termination phase: shuffling
% 6.69/2.33
% 6.69/2.33 % (1561)Memory used [KB]: 2046
% 6.69/2.33 % (1561)Time elapsed: 0.017 s
% 6.69/2.33 % (1561)Instructions burned: 31 (million)
% 6.69/2.33 % (1561)------------------------------
% 6.69/2.33 % (1561)------------------------------
% 6.69/2.33 % (1552)Instruction limit reached!
% 6.69/2.33 % (1552)------------------------------
% 6.69/2.33 % (1552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.33 % (1552)Termination reason: Unknown
% 6.69/2.33 % (1552)Termination phase: Saturation
% 6.69/2.33
% 6.69/2.33 % (1552)Memory used [KB]: 10746
% 6.69/2.33 % (1552)Time elapsed: 0.152 s
% 6.69/2.33 % (1552)Instructions burned: 508 (million)
% 6.69/2.33 % (1552)------------------------------
% 6.69/2.33 % (1552)------------------------------
% 6.69/2.34 % (1560)Instruction limit reached!
% 6.69/2.34 % (1560)------------------------------
% 6.69/2.34 % (1560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.34 % (1560)Termination reason: Unknown
% 6.69/2.34 % (1560)Termination phase: shuffling
% 6.69/2.34
% 6.69/2.34 % (1560)Memory used [KB]: 2686
% 6.69/2.34 % (1560)Time elapsed: 0.031 s
% 6.69/2.34 % (1560)Instructions burned: 62 (million)
% 6.69/2.34 % (1560)------------------------------
% 6.69/2.34 % (1560)------------------------------
% 6.69/2.34 % (1563)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/453Mi)
% 6.69/2.35 % (1564)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/71Mi)
% 6.69/2.36 % (1549)Instruction limit reached!
% 6.69/2.36 % (1549)------------------------------
% 6.69/2.36 % (1549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.36 % (1549)Termination reason: Unknown
% 6.69/2.36 % (1549)Termination phase: Saturation
% 6.69/2.36
% 6.69/2.36 % (1549)Memory used [KB]: 8955
% 6.69/2.36 % (1549)Time elapsed: 0.208 s
% 6.69/2.36 % (1549)Instructions burned: 448 (million)
% 6.69/2.36 % (1549)------------------------------
% 6.69/2.36 % (1549)------------------------------
% 6.69/2.37 % (1562)Instruction limit reached!
% 6.69/2.37 % (1562)------------------------------
% 6.69/2.37 % (1562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.37 % (1562)Termination reason: Unknown
% 6.69/2.37 % (1562)Termination phase: Preprocessing 3
% 6.69/2.37
% 6.69/2.37 % (1562)Memory used [KB]: 2942
% 6.69/2.37 % (1562)Time elapsed: 0.048 s
% 6.69/2.37 % (1562)Instructions burned: 96 (million)
% 6.69/2.37 % (1562)------------------------------
% 6.69/2.37 % (1562)------------------------------
% 6.69/2.37 % (1565)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/83Mi)
% 6.69/2.37 % (1566)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/11Mi)
% 6.69/2.38 % (1566)Instruction limit reached!
% 6.69/2.38 % (1566)------------------------------
% 6.69/2.38 % (1566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.38 % (1566)Termination reason: Unknown
% 6.69/2.38 % (1566)Termination phase: shuffling
% 6.69/2.38
% 6.69/2.38 % (1566)Memory used [KB]: 1663
% 6.69/2.38 % (1566)Time elapsed: 0.007 s
% 6.69/2.38 % (1566)Instructions burned: 11 (million)
% 6.69/2.38 % (1566)------------------------------
% 6.69/2.38 % (1566)------------------------------
% 6.69/2.39 % (1567)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/41Mi)
% 6.69/2.39 % (1564)Instruction limit reached!
% 6.69/2.39 % (1564)------------------------------
% 6.69/2.39 % (1564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.39 % (1564)Termination reason: Unknown
% 6.69/2.39 % (1564)Termination phase: Property scanning
% 6.69/2.39
% 6.69/2.39 % (1564)Memory used [KB]: 2814
% 6.69/2.39 % (1564)Time elapsed: 0.036 s
% 6.69/2.39 % (1564)Instructions burned: 71 (million)
% 6.69/2.39 % (1564)------------------------------
% 6.69/2.39 % (1564)------------------------------
% 6.69/2.40 % (1565)Instruction limit reached!
% 6.69/2.40 % (1565)------------------------------
% 6.69/2.40 % (1565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.69/2.40 % (1565)Termination reason: Unknown
% 6.69/2.40 % (1565)Termination phase: SInE selection
% 6.69/2.40
% 6.69/2.40 % (1565)Memory used [KB]: 2558
% 6.69/2.40 % (1565)Time elapsed: 0.027 s
% 6.69/2.40 % (1565)Instructions burned: 85 (million)
% 6.69/2.40 % (1565)------------------------------
% 6.69/2.40 % (1565)------------------------------
% 7.41/2.40 % (1568)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/6Mi)
% 7.41/2.40 % (1568)Instruction limit reached!
% 7.41/2.40 % (1568)------------------------------
% 7.41/2.40 % (1568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.40 % (1568)Termination reason: Unknown
% 7.41/2.40 % (1568)Termination phase: shuffling
% 7.41/2.40
% 7.41/2.40 % (1568)Memory used [KB]: 1535
% 7.41/2.40 % (1568)Time elapsed: 0.005 s
% 7.41/2.40 % (1568)Instructions burned: 6 (million)
% 7.41/2.40 % (1568)------------------------------
% 7.41/2.40 % (1568)------------------------------
% 7.41/2.40 % (1569)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/150Mi)
% 7.41/2.40 % (1567)Instruction limit reached!
% 7.41/2.40 % (1567)------------------------------
% 7.41/2.40 % (1567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.40 % (1567)Termination reason: Unknown
% 7.41/2.40 % (1567)Termination phase: shuffling
% 7.41/2.40
% 7.41/2.40 % (1567)Memory used [KB]: 2302
% 7.41/2.40 % (1567)Time elapsed: 0.021 s
% 7.41/2.40 % (1567)Instructions burned: 41 (million)
% 7.41/2.40 % (1567)------------------------------
% 7.41/2.40 % (1567)------------------------------
% 7.41/2.41 % (1570)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1352 for (2993ds/343Mi)
% 7.41/2.41 % (1556)First to succeed.
% 7.41/2.41 % (1556)Refutation found. Thanks to Tanya!
% 7.41/2.41 % SZS status Theorem for DTF2THF_1352
% 7.41/2.41 % SZS output start Proof for DTF2THF_1352
% 7.41/2.41 thf(type_def_6, type, proces554692349s_term: ($tType * $tType) > $tType).
% 7.41/2.41 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 7.41/2.41 thf(type_def_8, type, proces634752977rocess: ($tType) > $tType).
% 7.41/2.41 thf(type_def_9, type, set: ($tType) > $tType).
% 7.41/2.41 thf(type_def_10, type, itself: ($tType) > $tType).
% 7.41/2.41 thf(type_def_11, type, a: $tType).
% 7.41/2.41 thf(type_def_12, type, b: $tType).
% 7.41/2.41 thf(func_def_0, type, proces554692349s_term: ($tType * $tType) > $tType).
% 7.41/2.41 thf(func_def_1, type, proces634752977rocess: ($tType) > $tType).
% 7.41/2.41 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 7.41/2.41 thf(func_def_3, type, set: ($tType) > $tType).
% 7.41/2.41 thf(func_def_4, type, itself: ($tType) > $tType).
% 7.41/2.41 thf(func_def_5, type, b: $tType).
% 7.41/2.41 thf(func_def_6, type, a: $tType).
% 7.41/2.41 thf(func_def_7, type, undefined: !>[X0: $tType]:(X0)).
% 7.41/2.41 thf(func_def_8, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 7.41/2.41 thf(func_def_9, type, bot_bot: !>[X0: $tType]:(X0)).
% 7.41/2.41 thf(func_def_10, type, proces1239275103le_CH1: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 7.41/2.41 thf(func_def_11, type, proces1869379930H1_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 7.41/2.41 thf(func_def_12, type, proces1239275104le_CH2: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 7.41/2.41 thf(func_def_13, type, proces93903513H2_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 7.41/2.41 thf(func_def_14, type, proces126235999e_CONT: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 7.41/2.41 thf(func_def_15, type, proces1004198490NT_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 7.41/2.41 thf(func_def_16, type, proces1708129104e_PREF: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X1 @ X0 > X1)).
% 7.41/2.41 thf(func_def_17, type, proces527360425EF_rel: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > $o)).
% 7.41/2.41 thf(func_def_18, type, proces1121166967uarded: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > $o)).
% 7.41/2.41 thf(func_def_19, type, proces687458811_isACT: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X3 @ X0 > $o)).
% 7.41/2.41 thf(func_def_20, type, proces896239806CT_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > $o)).
% 7.41/2.41 thf(func_def_21, type, proces1525233512Action: !>[X0: $tType]:(X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_22, type, proces1915862579Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_23, type, proces1406508781rocess: !>[X0: $tType, X1: $tType]:((X0 > proces634752977rocess @ X0 > X1) > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > X1) > proces634752977rocess @ X0 > X1)).
% 7.41/2.41 thf(func_def_24, type, proces979765041_ch1Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_25, type, proces988026546_ch2Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_26, type, proces1778668539contOf: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_27, type, proces894737309rocess: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > X0 > proces634752977rocess @ X1)).
% 7.41/2.41 thf(func_def_28, type, proces10484146Action: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_29, type, proces401113213Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_30, type, proces370407749rocess: !>[X0: $tType, X1: $tType]:((X0 > X1) > proces634752977rocess @ X0 > proces634752977rocess @ X1)).
% 7.41/2.41 thf(func_def_31, type, proces745025900prefOf: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 7.41/2.41 thf(func_def_32, type, proces749077512rocess: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o)).
% 7.41/2.41 thf(func_def_33, type, proces1148692671rocess: !>[X0: $tType]:(proces634752977rocess @ X0 > set @ X0)).
% 7.41/2.41 thf(func_def_34, type, proces1454156180ss_ACT: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 7.41/2.41 thf(func_def_35, type, proces89589571ess_CH: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 7.41/2.41 thf(func_def_36, type, proces1062592052s_PROC: !>[X0: $tType, X1: $tType]:(proces634752977rocess @ X0 > proces554692349s_term @ X0 @ X1)).
% 7.41/2.41 thf(func_def_37, type, proces1627516585ss_VAR: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X1 @ X0)).
% 7.41/2.41 thf(func_def_38, type, proces460752237s_term: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (proces634752977rocess @ X2 > X1) > (X2 > proces554692349s_term @ X2 @ X0 > X1) > (proces554692349s_term @ X2 @ X0 > proces554692349s_term @ X2 @ X0 > X1) > proces554692349s_term @ X2 @ X0 > X1)).
% 7.41/2.41 thf(func_def_39, type, proces224683037s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3)).
% 7.41/2.41 thf(func_def_40, type, proces2118920028s_term: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > proces554692349s_term @ X0 @ X1 > $o)).
% 7.41/2.41 thf(func_def_41, type, proces2029722208s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3 > $o)).
% 7.41/2.41 thf(func_def_42, type, proces1264666542s_term: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > set @ X0)).
% 7.41/2.41 thf(func_def_43, type, proces1493547885s_term: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > set @ X1)).
% 7.41/2.41 thf(func_def_44, type, proces1652378886lution: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 7.41/2.41 thf(func_def_45, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 7.41/2.41 thf(func_def_46, type, type: !>[X0: $tType]:(itself @ X0)).
% 7.41/2.41 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 7.41/2.41 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 7.41/2.41 thf(func_def_49, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 7.41/2.41 thf(func_def_50, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 7.41/2.41 thf(func_def_51, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 7.41/2.41 thf(func_def_52, type, p: proces634752977rocess @ a).
% 7.41/2.41 thf(func_def_53, type, p2: proces634752977rocess @ a).
% 7.41/2.41 thf(func_def_54, type, pa: proces634752977rocess @ a).
% 7.41/2.41 thf(func_def_55, type, q: proces634752977rocess @ a).
% 7.41/2.41 thf(func_def_56, type, sys: b > proces554692349s_term @ a @ b).
% 7.41/2.41 thf(func_def_80, type, sP0: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_81, type, sP1: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_82, type, sP2: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_83, type, sP3: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_84, type, sP4: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_85, type, sP5: !>[X0: $tType, X1: $tType]:((proces634752977rocess @ X1 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X1 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_86, type, sP6: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (proces634752977rocess @ X1 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X1 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_87, type, sP7: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_88, type, sP8: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_89, type, sP9: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 7.41/2.41 thf(func_def_90, type, sP10: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 7.41/2.41 thf(func_def_91, type, sP11: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_92, type, sP12: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_93, type, sP13: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > X0 > X0 > $o)).
% 7.41/2.41 thf(func_def_94, type, sP14: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_95, type, sP15: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o)).
% 7.41/2.41 thf(func_def_96, type, sP16: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 7.41/2.41 thf(func_def_97, type, sP17: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 7.41/2.41 thf(func_def_98, type, sK18: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_99, type, sK19: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_100, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_101, type, sK21: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o) > proces634752977rocess @ X1)).
% 7.41/2.41 thf(func_def_102, type, sK22: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_103, type, sK23: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_104, type, sK24: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 7.41/2.41 thf(func_def_105, type, sK25: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 7.41/2.41 thf(func_def_106, type, sK26: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_107, type, sK27: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_108, type, sK28: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_109, type, sK29: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_110, type, sK30: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_111, type, sK31: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_112, type, sK32: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_113, type, sK33: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_114, type, sK34: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 7.41/2.41 thf(func_def_115, type, sK35: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 7.41/2.41 thf(func_def_116, type, sK36: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 7.41/2.41 thf(func_def_117, type, sK37: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_118, type, sK38: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_119, type, sK39: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_120, type, sK40: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_121, type, sK41: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_122, type, sK42: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_123, type, sK43: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_124, type, sK44: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 7.41/2.41 thf(func_def_126, type, ph46: !>[X0: $tType]:(X0)).
% 7.41/2.41 thf(f1373,plain,(
% 7.41/2.41 $false),
% 7.41/2.41 inference(avatar_sat_refutation,[status(thm)],[f974,f981,f982,f1260,f1272,f1285,f1288,f1294,f1335,f1357,f1359,f1372])).
% 7.41/2.41 thf(f1372,plain,(
% 7.41/2.41 ~spl45_1 | ~spl45_2),
% 7.41/2.41 inference(avatar_contradiction_clause,[status(thm)],[f1371])).
% 7.41/2.41 thf(f1371,plain,(
% 7.41/2.41 $false | (~spl45_1 | ~spl45_2)),
% 7.41/2.41 inference(subsumption_resolution,[status(thm)],[f1304,f960])).
% 7.41/2.41 thf(f960,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ~spl45_2),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f959])).
% 7.41/2.41 thf(f959,definition,(
% 7.41/2.41 spl45_2 <=> ((proces10484146Action @ a @ pa) = $true)),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_2])],[avatar_definition])).
% 7.41/2.41 thf(f1304,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) != $true) | ~spl45_1),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1303])).
% 7.41/2.41 thf(f1303,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) != $true) | ($true != $true) | ~spl45_1),
% 7.41/2.41 inference(superposition,[status(thm)],[f888,f957])).
% 7.41/2.41 thf(f957,plain,(
% 7.41/2.41 ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) = $true) | ~spl45_1),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f956])).
% 7.41/2.41 thf(f956,definition,(
% 7.41/2.41 spl45_1 <=> ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) = $true)),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_1])],[avatar_definition])).
% 7.41/2.41 thf(f888,plain,(
% 7.41/2.41 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces1406508781rocess @ X0 @ $o @ (^[Y0 : X0]: ((^[Y1 : proces634752977rocess @ X0]: ($false)))) @ (^[Y0 : proces634752977rocess @ X0]: ((^[Y1 : proces634752977rocess @ X0]: ($true)))) @ X1) != $true) | ((proces10484146Action @ X0 @ X1) != $true)) )),
% 7.41/2.41 inference(definition_unfolding,[status(thm)],[f810,f836])).
% 7.41/2.41 thf(f836,plain,(
% 7.41/2.41 ( ! [X0 : $tType] : ((proces401113213Choice @ X0 = (proces1406508781rocess @ X0 @ $o @ (^[Y0 : X0]: ((^[Y1 : proces634752977rocess @ X0]: ($false)))) @ (^[Y0 : proces634752977rocess @ X0]: ((^[Y1 : proces634752977rocess @ X0]: ($true))))))) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f335])).
% 7.41/2.41 thf(f335,plain,(
% 7.41/2.41 ! [X0 : $tType] : (proces401113213Choice @ X0 = (proces1406508781rocess @ X0 @ $o @ (^[Y0 : X0]: ((^[Y1 : proces634752977rocess @ X0]: ($false)))) @ (^[Y0 : proces634752977rocess @ X0]: ((^[Y1 : proces634752977rocess @ X0]: ($true))))))),
% 7.41/2.41 inference(fool_elimination,[status(thm)],[f334])).
% 7.41/2.41 thf(f334,plain,(
% 7.41/2.41 ! [X0 : $tType] : (proces401113213Choice @ X0 = (proces1406508781rocess @ X0 @ $o @ (^[X1 : X0, X2 : proces634752977rocess @ X0] : ($false)) @ (^[X3 : proces634752977rocess @ X0, X4 : proces634752977rocess @ X0] : ($true))))),
% 7.41/2.41 inference(rectify,[status(thm)],[f45])).
% 7.41/2.41 thf(f45,axiom,(
% 7.41/2.41 ! [X0 : $tType] : (proces401113213Choice @ X0 = (proces1406508781rocess @ X0 @ $o @ (^[X65 : X0, X66 : proces634752977rocess @ X0] : ($false)) @ (^[X65 : proces634752977rocess @ X0, X66 : proces634752977rocess @ X0] : ($true))))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_44_process_Odisc__eq__case_I2_J)).
% 7.41/2.41 thf(f810,plain,(
% 7.41/2.41 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces401113213Choice @ X0 @ X1) != $true) | ((proces10484146Action @ X0 @ X1) != $true)) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f670])).
% 7.41/2.41 thf(f670,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces401113213Choice @ X0 @ X1) != $true) | ((proces10484146Action @ X0 @ X1) != $true))),
% 7.41/2.41 inference(ennf_transformation,[status(thm)],[f660])).
% 7.41/2.41 thf(f660,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces401113213Choice @ X0 @ X1) = $true) => ((proces10484146Action @ X0 @ X1) != $true))),
% 7.41/2.41 inference(flattening,[status(thm)],[f373])).
% 7.41/2.41 thf(f373,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces401113213Choice @ X0 @ X1) = $true) => ~((proces10484146Action @ X0 @ X1) = $true))),
% 7.41/2.41 inference(fool_elimination,[status(thm)],[f372])).
% 7.41/2.41 thf(f372,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : ((proces401113213Choice @ X0 @ X1) => ~(proces10484146Action @ X0 @ X1))),
% 7.41/2.41 inference(rectify,[status(thm)],[f2])).
% 7.41/2.41 thf(f2,axiom,(
% 7.41/2.41 ! [X0 : $tType,X7 : proces634752977rocess @ X0] : ((proces401113213Choice @ X0 @ X7) => ~(proces10484146Action @ X0 @ X7))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_1_process_Odistinct__disc_I2_J)).
% 7.41/2.41 thf(f1359,plain,(
% 7.41/2.41 spl45_2 | ~spl45_3),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f1351,f962,f959])).
% 7.41/2.41 thf(f962,definition,(
% 7.41/2.41 spl45_3 <=> ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true)),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_3])],[avatar_definition])).
% 7.41/2.41 thf(f1351,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ~spl45_3),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1349])).
% 7.41/2.41 thf(f1349,plain,(
% 7.41/2.41 ($false = $true) | ((proces10484146Action @ a @ pa) = $true) | ~spl45_3),
% 7.41/2.41 inference(superposition,[status(thm)],[f933,f1343])).
% 7.41/2.41 thf(f1343,plain,(
% 7.41/2.41 ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) = $true) | ~spl45_3),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1341])).
% 7.41/2.41 thf(f1341,plain,(
% 7.41/2.41 ($false = $true) | ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) = $true) | ~spl45_3),
% 7.41/2.41 inference(superposition,[status(thm)],[f953,f963])).
% 7.41/2.41 thf(f963,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true) | ~spl45_3),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f962])).
% 7.41/2.41 thf(f953,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (($false = (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3))) | ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) = $true)) )),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f852])).
% 7.41/2.41 thf(f852,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) = (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)))) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f658])).
% 7.41/2.41 thf(f658,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) = (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)))),
% 7.41/2.41 inference(rectify,[status(thm)],[f37])).
% 7.41/2.41 thf(f37,axiom,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X63 : X0 > proces554692349s_term @ X1 @ X0,X64 : proces554692349s_term @ X1 @ X0] : ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X63 @ X64) = (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X63 @ X64)))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_36_solution_Odisc__iff_I1_J)).
% 7.41/2.41 thf(f933,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : (($false = (proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5))) | ((proces10484146Action @ X3 @ X5) = $true)) )),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f873])).
% 7.41/2.41 thf(f873,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : (((proces10484146Action @ X3 @ X5) = (proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5)))) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f659])).
% 7.41/2.41 thf(f659,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : ((proces10484146Action @ X3 @ X5) = (proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5)))),
% 7.41/2.41 inference(rectify,[status(thm)],[f43])).
% 7.41/2.41 thf(f43,axiom,(
% 7.41/2.41 ! [X0 : $tType,X2 : $tType,X1 : $tType,X3 : $tType,X63 : X0 > proces554692349s_term @ X1 @ X2,X8 : proces634752977rocess @ X3] : ((proces687458811_isACT @ X0 @ X1 @ X2 @ X3 @ X63 @ (proces1062592052s_PROC @ X3 @ X0 @ X8)) = (proces10484146Action @ X3 @ X8))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_42_isACT_Osimps_I2_J)).
% 7.41/2.41 thf(f1357,plain,(
% 7.41/2.41 ~spl45_3 | ~spl45_8),
% 7.41/2.41 inference(avatar_contradiction_clause,[status(thm)],[f1356])).
% 7.41/2.41 thf(f1356,plain,(
% 7.41/2.41 $false | (~spl45_3 | ~spl45_8)),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1355])).
% 7.41/2.41 thf(f1355,plain,(
% 7.41/2.41 ($false = $true) | (~spl45_3 | ~spl45_8)),
% 7.41/2.41 inference(forward_demodulation,[status(thm)],[f1350,f980])).
% 7.41/2.41 thf(f980,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $false) | ~spl45_8),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f979])).
% 7.41/2.41 thf(f979,definition,(
% 7.41/2.41 spl45_8 <=> ((proces10484146Action @ a @ pa) = $false)),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_8])],[avatar_definition])).
% 7.41/2.41 thf(f1350,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ~spl45_3),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1348])).
% 7.41/2.41 thf(f1348,plain,(
% 7.41/2.41 ($false = $true) | ((proces10484146Action @ a @ pa) = $true) | ~spl45_3),
% 7.41/2.41 inference(superposition,[status(thm)],[f1343,f933])).
% 7.41/2.41 thf(f1335,plain,(
% 7.41/2.41 spl45_3 | ~spl45_6),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f1332,f972,f962])).
% 7.41/2.41 thf(f972,definition,(
% 7.41/2.41 spl45_6 <=> ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_6])],[avatar_definition])).
% 7.41/2.41 thf(f1332,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true) | ~spl45_6),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1331])).
% 7.41/2.41 thf(f1331,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true) | ($false = $true) | ~spl45_6),
% 7.41/2.41 inference(superposition,[status(thm)],[f883,f973])).
% 7.41/2.41 thf(f973,plain,(
% 7.41/2.41 ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ~spl45_6),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f972])).
% 7.41/2.41 thf(f883,plain,(
% 7.41/2.41 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces1406508781rocess @ X0 @ $o @ (^[Y0 : X0]: ((^[Y1 : proces634752977rocess @ X0]: ($false)))) @ (^[Y0 : proces634752977rocess @ X0]: ((^[Y1 : proces634752977rocess @ X0]: ($true)))) @ X1) = $true) | ((proces10484146Action @ X0 @ X1) = $true)) )),
% 7.41/2.41 inference(definition_unfolding,[status(thm)],[f790,f836])).
% 7.41/2.41 thf(f790,plain,(
% 7.41/2.41 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces10484146Action @ X0 @ X1) = $true) | ((proces401113213Choice @ X0 @ X1) = $true)) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f690])).
% 7.41/2.41 thf(f690,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces10484146Action @ X0 @ X1) = $true) | ((proces401113213Choice @ X0 @ X1) = $true))),
% 7.41/2.41 inference(ennf_transformation,[status(thm)],[f661])).
% 7.41/2.41 thf(f661,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (((proces10484146Action @ X0 @ X1) != $true) => ((proces401113213Choice @ X0 @ X1) = $true))),
% 7.41/2.41 inference(flattening,[status(thm)],[f343])).
% 7.41/2.41 thf(f343,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (~((proces10484146Action @ X0 @ X1) = $true) => ((proces401113213Choice @ X0 @ X1) = $true))),
% 7.41/2.41 inference(fool_elimination,[status(thm)],[f342])).
% 7.41/2.41 thf(f342,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (~(proces10484146Action @ X0 @ X1) => (proces401113213Choice @ X0 @ X1))),
% 7.41/2.41 inference(rectify,[status(thm)],[f5])).
% 7.41/2.41 thf(f5,axiom,(
% 7.41/2.41 ! [X0 : $tType,X7 : proces634752977rocess @ X0] : (~(proces10484146Action @ X0 @ X7) => (proces401113213Choice @ X0 @ X7))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_4_process_Oexhaust__disc)).
% 7.41/2.41 thf(f1294,plain,(
% 7.41/2.41 ~spl45_5 | ~spl45_8),
% 7.41/2.41 inference(avatar_contradiction_clause,[status(thm)],[f1293])).
% 7.41/2.41 thf(f1293,plain,(
% 7.41/2.41 $false | (~spl45_5 | ~spl45_8)),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1292])).
% 7.41/2.41 thf(f1292,plain,(
% 7.41/2.41 ($false = $true) | (~spl45_5 | ~spl45_8)),
% 7.41/2.41 inference(forward_demodulation,[status(thm)],[f1236,f980])).
% 7.41/2.41 thf(f1236,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ~spl45_5),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1235])).
% 7.41/2.41 thf(f1235,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ($false = $true) | ~spl45_5),
% 7.41/2.41 inference(superposition,[status(thm)],[f970,f883])).
% 7.41/2.41 thf(f970,plain,(
% 7.41/2.41 ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa)) | ~spl45_5),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f969])).
% 7.41/2.41 thf(f969,definition,(
% 7.41/2.41 spl45_5 <=> ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa))),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_5])],[avatar_definition])).
% 7.41/2.41 thf(f1288,plain,(
% 7.41/2.41 ~spl45_1 | ~spl45_5),
% 7.41/2.41 inference(avatar_contradiction_clause,[status(thm)],[f1287])).
% 7.41/2.41 thf(f1287,plain,(
% 7.41/2.41 $false | (~spl45_1 | ~spl45_5)),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1286])).
% 7.41/2.41 thf(f1286,plain,(
% 7.41/2.41 ($false = $true) | (~spl45_1 | ~spl45_5)),
% 7.41/2.41 inference(forward_demodulation,[status(thm)],[f957,f970])).
% 7.41/2.41 thf(f1285,plain,(
% 7.41/2.41 ~spl45_2 | ~spl45_8),
% 7.41/2.41 inference(avatar_contradiction_clause,[status(thm)],[f1284])).
% 7.41/2.41 thf(f1284,plain,(
% 7.41/2.41 $false | (~spl45_2 | ~spl45_8)),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1283])).
% 7.41/2.41 thf(f1283,plain,(
% 7.41/2.41 ($false = $true) | (~spl45_2 | ~spl45_8)),
% 7.41/2.41 inference(backward_demodulation,[status(thm)],[f960,f980])).
% 7.41/2.41 thf(f1272,plain,(
% 7.41/2.41 spl45_8 | ~spl45_7),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f1271,f976,f979])).
% 7.41/2.41 thf(f976,definition,(
% 7.41/2.41 spl45_7 <=> ($false = (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_7])],[avatar_definition])).
% 7.41/2.41 thf(f1271,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $false) | ~spl45_7),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1269])).
% 7.41/2.41 thf(f1269,plain,(
% 7.41/2.41 ($true != $true) | ((proces10484146Action @ a @ pa) = $false) | ~spl45_7),
% 7.41/2.41 inference(superposition,[status(thm)],[f1265,f934])).
% 7.41/2.41 thf(f934,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : (((proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5)) = $true) | ($false = (proces10484146Action @ X3 @ X5))) )),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f873])).
% 7.41/2.41 thf(f1265,plain,(
% 7.41/2.41 ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) != $true) | ~spl45_7),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1264])).
% 7.41/2.41 thf(f1264,plain,(
% 7.41/2.41 ($false = $true) | ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) != $true) | ~spl45_7),
% 7.41/2.41 inference(superposition,[status(thm)],[f856,f977])).
% 7.41/2.41 thf(f977,plain,(
% 7.41/2.41 ($false = (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ~spl45_7),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f976])).
% 7.41/2.41 thf(f856,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (((proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)) = $true) | ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) != $true)) )),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f687])).
% 7.41/2.41 thf(f687,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) != $true) | ((proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)) = $true))),
% 7.41/2.41 inference(ennf_transformation,[status(thm)],[f649])).
% 7.41/2.41 thf(f649,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) = $true) => ((proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)) = $true))),
% 7.41/2.41 inference(fool_elimination,[status(thm)],[f648])).
% 7.41/2.41 thf(f648,plain,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3) => (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)))),
% 7.41/2.41 inference(rectify,[status(thm)],[f39])).
% 7.41/2.41 thf(f39,axiom,(
% 7.41/2.41 ! [X0 : $tType,X1 : $tType,X63 : X0 > proces554692349s_term @ X1 @ X0,X64 : proces554692349s_term @ X1 @ X0] : ((proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X63 @ X64) => (proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X63 @ X64)))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_38_solution_Odisc_I1_J)).
% 7.41/2.41 thf(f1260,plain,(
% 7.41/2.41 spl45_8 | ~spl45_4),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f1257,f965,f979])).
% 7.41/2.41 thf(f965,definition,(
% 7.41/2.41 spl45_4 <=> ($true = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 7.41/2.41 introduced(definition,[new_symbols(naming,[spl45_4])],[avatar_definition])).
% 7.41/2.41 thf(f1257,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $false) | ~spl45_4),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1255])).
% 7.41/2.41 thf(f1255,plain,(
% 7.41/2.41 ($false = $true) | ((proces10484146Action @ a @ pa) = $false) | ~spl45_4),
% 7.41/2.41 inference(superposition,[status(thm)],[f1253,f934])).
% 7.41/2.41 thf(f1253,plain,(
% 7.41/2.41 ($false = (proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) | ~spl45_4),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1249])).
% 7.41/2.41 thf(f1249,plain,(
% 7.41/2.41 ($false = (proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) | ($true != $true) | ~spl45_4),
% 7.41/2.41 inference(superposition,[status(thm)],[f1248,f954])).
% 7.41/2.41 thf(f954,plain,(
% 7.41/2.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces554692349s_term @ X1 @ X0] : (((proces10484146Action @ X1 @ (proces1652378886lution @ X0 @ X1 @ X2 @ X3)) = $true) | ($false = (proces687458811_isACT @ X0 @ X1 @ X0 @ X1 @ X2 @ X3))) )),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f852])).
% 7.41/2.41 thf(f1248,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) != $true) | ~spl45_4),
% 7.41/2.41 inference(trivial_inequality_removal,[status(thm)],[f1246])).
% 7.41/2.41 thf(f1246,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) != $true) | ($true != $true) | ~spl45_4),
% 7.41/2.41 inference(superposition,[status(thm)],[f888,f966])).
% 7.41/2.41 thf(f966,plain,(
% 7.41/2.41 ($true = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ~spl45_4),
% 7.41/2.41 inference(avatar_component_clause,[status(thm)],[f965])).
% 7.41/2.41 thf(f982,plain,(
% 7.41/2.41 spl45_5 | spl45_8 | spl45_6 | spl45_7),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f940,f976,f972,f979,f969])).
% 7.41/2.41 thf(f940,plain,(
% 7.41/2.41 ($false = (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa)) | ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ((proces10484146Action @ a @ pa) = $false)),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f938])).
% 7.41/2.41 thf(f938,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $false) | ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) != (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ($false = (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f894])).
% 7.41/2.41 thf(f894,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) != (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) != (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 7.41/2.41 inference(definition_unfolding,[status(thm)],[f825,f836,f836,f821,f821])).
% 7.41/2.41 thf(f821,plain,(
% 7.41/2.41 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f9])).
% 7.41/2.41 thf(f9,axiom,(
% 7.41/2.41 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',fact_8_iss)).
% 7.41/2.41 thf(f825,plain,(
% 7.41/2.41 ((proces401113213Choice @ a @ pa) != (proces401113213Choice @ a @ p2)) | ((proces10484146Action @ a @ pa) != (proces10484146Action @ a @ p2))),
% 7.41/2.41 inference(cnf_transformation,[status(thm)],[f700])).
% 7.41/2.41 thf(f700,plain,(
% 7.41/2.41 ((proces401113213Choice @ a @ pa) != (proces401113213Choice @ a @ p2)) | ((proces10484146Action @ a @ pa) != (proces10484146Action @ a @ p2))),
% 7.41/2.41 inference(ennf_transformation,[status(thm)],[f260])).
% 7.41/2.41 thf(f260,negated_conjecture,(
% 7.41/2.41 ~(((proces10484146Action @ a @ pa) = (proces10484146Action @ a @ p2)) & ((proces401113213Choice @ a @ pa) = (proces401113213Choice @ a @ p2)))),
% 7.41/2.41 inference(negated_conjecture,[status(cth)],[f259])).
% 7.41/2.41 thf(f259,conjecture,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = (proces10484146Action @ a @ p2)) & ((proces401113213Choice @ a @ pa) = (proces401113213Choice @ a @ p2))),
% 7.41/2.41 file('/export/starexec/sandbox/tmp/tmp.ij59LFwLny/DTF2THF_1352.p',conj_0)).
% 7.41/2.41 thf(f981,plain,(
% 7.41/2.41 spl45_7 | spl45_1 | spl45_8 | spl45_4),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f939,f965,f979,f956,f976])).
% 7.41/2.41 thf(f939,plain,(
% 7.41/2.41 ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) = $true) | ($true = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ($false = (proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ((proces10484146Action @ a @ pa) = $false)),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f938])).
% 7.41/2.41 thf(f974,plain,(
% 7.41/2.41 spl45_5 | spl45_2 | spl45_3 | spl45_6),
% 7.41/2.41 inference(avatar_split_clause,[status(thm)],[f942,f972,f962,f959,f969])).
% 7.41/2.41 thf(f942,plain,(
% 7.41/2.41 ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa)) | ((proces10484146Action @ a @ pa) = $true) | ($false = (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true)),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f937])).
% 7.41/2.41 thf(f937,plain,(
% 7.41/2.41 ((proces10484146Action @ a @ pa) = $true) | ((proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ pa) != (proces1406508781rocess @ a @ $o @ (^[Y0 : a]: ((^[Y1 : proces634752977rocess @ a]: ($false)))) @ (^[Y0 : proces634752977rocess @ a]: ((^[Y1 : proces634752977rocess @ a]: ($true)))) @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ((proces10484146Action @ a @ (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) = $true)),
% 7.41/2.41 inference(binary_proxy_clausification,[status(thm)],[f894])).
% 7.41/2.41 % SZS output end Proof for DTF2THF_1352
% 7.41/2.41 % (1556)------------------------------
% 7.41/2.41 % (1556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.41 % (1556)Termination reason: Refutation
% 7.41/2.41
% 7.41/2.41 % (1556)Memory used [KB]: 7803
% 7.41/2.41 % (1556)Time elapsed: 0.143 s
% 7.41/2.41 % (1556)Instructions burned: 276 (million)
% 7.41/2.41 % (1556)------------------------------
% 7.41/2.41 % (1556)------------------------------
% 7.41/2.41 % (1506)Success in time 0.678 s
%------------------------------------------------------------------------------